WO2022262007A1

WO2022262007A1 - Graph algorithm autoincrement method and apparatus, device, and storage medium

Info

Publication number: WO2022262007A1
Application number: PCT/CN2021/102218
Authority: WO
Inventors: 樊文飞; 田超; 许瑞琦; 尹强; 于文渊; 周靖人
Original assignee: 深圳计算科学研究院
Priority date: 2021-06-18
Filing date: 2021-06-24
Publication date: 2022-12-22
Also published as: CN113343040A

Abstract

A graph algorithm autoincrement method and apparatus, a device, and a storage medium, the method comprising: acquiring a batch processing graph algorithm (S110); when the batch processing graph algorithm is a fixed point calculation, acquiring a step function of the batch processing graph algorithm from the data structure and logic of the batch processing graph algorithm for the fixed point calculation; according to the data structure and logic of the batch processing graph algorithm, generating an initial range function based on a graph update region; and combining the initial range function and the step function to obtain an incremental processing algorithm corresponding to the batch processing algorithm (S120); or, when the batch processing graph algorithm is a fixed point calculation, determining whether the batch processing graph algorithm has bounded incremental properties; and, when the batch processing graph algorithm has bounded incremental properties, converting the batch processing algorithm into an incremental processing algorithm, the incremental processing algorithm having bounded incremental properties (S130). In the present method, incremental calculation can be performed in a manner more efficient than batch recomputing.

Description

Automatic increment method, device, equipment and storage medium of graph algorithm

technical field

The present application relates to the technical field of data processing, in particular to a graph algorithm automatic increment method, device, equipment and storage medium.

Background technique

Queries on large graphs consume a lot of resources and time. To further complicate the situation, graph data is constantly changing, such as the values on vertices or the insertion and deletion of edge links, which makes some processes need to automatically and repeatedly query the changing graph data to obtain the latest query results. This process consumes a lot of computing resources, especially on large graphs.

In the above case, after the graph data is updated, the complexity of the batch query is still related to the size of the graph data itself, and has nothing to do with the size of the graph update. This method will become very inefficient when the graph data is large and the update frequency is frequent.

The existing incremental graph query algorithms are specially designed for specific problems. This method lacks versatility and requires a lot of professional knowledge, which greatly increases the threshold for using incremental algorithms. On the other hand, the main advancement of the existing incremental algorithms lies in the fact that for unit update (unitupdate), it has lower complexity compared with batch processing, but for batch update (batchupdate), the efficiency of these incremental algorithms is often Directly computing the updated graph without re-using the batch algorithm results in higher query results, and how to use incremental computation in a more efficient way than batch re-computation in this case is still an open problem.

Contents of the invention

In view of the above problems, this application is proposed to provide an automatic incremental method, device, device and storage medium for a graph algorithm that overcomes the above problems or at least partially solves the above problems, including:

An automatic incrementalization method for a graph algorithm, comprising:

Get the batch graph algorithm;

When the batch processing graph algorithm is a fixed point calculation, the batch processing graph algorithm is obtained from the data structure and logic of the batch processing graph algorithm as a step function of the fixed point calculation; according to the batch processing The data structure and logic of the graph algorithm generate an initial range function based on the graph update area; combine the initial range function and the step function to obtain an incremental processing algorithm corresponding to the batch processing algorithm;

or;

When the batch processing graph algorithm is a fixed point calculation, it is judged whether the batch processing graph algorithm has a bounded incremental property; when the batch processing graph algorithm has a bounded incremental property, then the The batch processing algorithm is transformed into an incremental processing algorithm, which has a bounded incremental property.

Preferably, it also includes:

Judging whether the batch processing graph algorithm is an iteration of a step function related to the graph, state, query result and range; wherein, the graph is an undirected graph; the state is the data structure of the batch processing graph algorithm The state at the beginning of the preset round; the query result is the query result obtained after using the batch graph algorithm to query the graph, the query result is composed of the state variables, and each of the state variables is Associated with a certain point or edge in the graph, each of the state variables has a corresponding update function for updating the value of the state variable, and the input of the update function is a set of the state variables , each of the state variables corresponds to a logic judgment statement, satisfying that after each update function is used to update the state variable, the logic judgment statement is true, and for the final fixed point state, all the logic The judgment statement is all true; the range includes the state variables that all correspond to the logic judgment statement being negated when the preset round starts;

If the batch graph algorithm is an iteration of a step function related to the state, the query result, the graph, and the range, then the batch graph algorithm is determined to be a fixed point computation.

Preferably, the step of generating the initial range function based on the graph update region according to the data structure and logic of the batch graph algorithm includes:

Obtaining a subset of the input of the update function in a fixed point state as an anchor set of the state variable;

Generate a directed acyclic graph according to the anchor set, the directed acyclic graph includes the topological partial order relationship of each point in the graph in the fixed point state, and the topological partial order relationship is used to guide the batch handles change propagation for graph algorithms;

The initial range function based on the graph update region is generated from the directed acyclic graph.

Preferably, after the step of combining the initial range function and the step function to obtain the incremental processing algorithm corresponding to the batch processing algorithm, it further includes:

Obtaining the query result and the update area of the graph;

modifying the fixed point state of the query result to an initial state feasible for the updated graph and an initial range on the initial state using the initial range function;

The step function is used to iterate the initial state and the initial range to a new fixed point to obtain a query result of the updated graph.

Preferably, it also includes:

When the batch graph algorithm does not have a bounded incremental property, determine whether the batch graph algorithm has a weakly incremental property;

When the batch processing graph algorithm has a weakly incremental property, the step function and the state of the batch processing graph algorithm are modified so that the batch processing graph algorithm has bounded incrementalization property; converting the batch processing algorithm into an incremental processing algorithm, and the incremental processing algorithm has a bounded incremental property.

Preferably, the step of converting the batch processing algorithm into an incremental processing algorithm includes:

deriving the batch graph algorithm as a step function for fixed point computation from the batch graph algorithm's data structure and logic;

Generate an initial range function based on the graph update region according to the data structure and logic of the batch graph algorithm;

Combining the initial range function and the step function to obtain an incremental processing algorithm corresponding to the batch processing algorithm.

Preferably, the batch graph algorithm includes any one of weakly connected component algorithm, single-source shortest path algorithm, depth-first search algorithm, local clustering coefficient algorithm and graph simulation algorithm.

An automatic incrementalization device for a graph algorithm, comprising:

Obtaining a module for obtaining a batch graph algorithm;

The first processing module is used to obtain the step of the batch graph algorithm as a fixed point calculation from the data structure and logic of the batch graph algorithm when the batch graph algorithm is a fixed point calculation function; generate an initial range function based on the graph update region according to the data structure and logic of the batch processing graph algorithm; combine the initial range function and the step function to obtain an increment corresponding to the batch processing algorithm processing algorithm;

or;

The second processing module is used to determine whether the batch graph algorithm has a bounded incremental property when the batch graph algorithm is a fixed point calculation; when the batch graph algorithm has a bounded incremental property When the property is , the batch processing algorithm is transformed into an incremental processing algorithm, and the incremental processing algorithm has a bounded incremental property.

A device comprising a processor, a memory, and a computer program stored on the memory and capable of running on the processor, the computer program implementing a graph algorithm as described above when executed by the processor The steps of the auto-increment method.

A computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the above-mentioned automatic increment method for a graph algorithm are realized.

This application has the following advantages:

In the embodiment of the present application, by obtaining the batch processing graph algorithm; when the batch processing graph algorithm is fixed point calculation, the batch processing graph algorithm is obtained from the data structure and logic of the batch processing graph algorithm As a step function for fixed point calculation; according to the data structure and logic of the batch graph algorithm, an initial range function based on the graph update area is generated; the initial range function and the step function are combined to obtain the same value as the original range function The incremental processing algorithm corresponding to the batch processing algorithm; or; when the batch processing graph algorithm is a fixed point calculation, judging whether the batch processing graph algorithm has a bounded incremental property; when the batch processing graph algorithm When it has a bounded incremental property, the batch processing algorithm is converted into an incremental processing algorithm, and the incremental processing algorithm has a bounded incremental property, which can obtain a more efficient way than batch recalculation for incremental processing. volume calculation.

Description of drawings

In order to illustrate the technical solution of the present application more clearly, the accompanying drawings that need to be used in the description of the present application will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. Ordinary technicians can also obtain other drawings based on these drawings on the premise of not paying creative work.

Fig. 1 is a flow chart of the steps of an automatic increment method of a graph algorithm provided by an embodiment of the present application;

Fig. 2 is a schematic structural diagram of a graph growth model that generates two-way edge segmentation in an automatic incremental method of a graph algorithm provided by an embodiment of the present application;

Fig. 3 is a structural block diagram of an automatic incrementing device for a graph algorithm provided by an embodiment of the present application;

Fig. 4 is a schematic structural diagram of a computer device provided by an embodiment of the present application.

12. Computer equipment; 14. Peripheral equipment; 16. Processing unit; 18. Bus; 20. Network adapter; 22. I/O interface; 24. Display; 28. Memory; 30. Random access memory; 32. Cache memory; 34, storage system; 40, program/utility tool; 42, program module.

detailed description

In order to make the purpose, features and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods. Apparently, the described embodiments are some of the embodiments of the present application, but not all of them. Based on the embodiments in this application, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of this application.

Referring to FIG. 1 , it shows an automatic increment method of a graph algorithm provided by an embodiment of the present application, including:

S110. Acquire the batch graph algorithm A;

S120. When the batch graph algorithm A is fixed point calculation, obtain the batch graph algorithm A as the step function f of the fixed point calculation from the data structure and logic of the batch graph algorithm A _A ; generate an initial range function h based on the graph update area ΔG according to the data structure and logic of the batch processing graph algorithm A; combine the initial range function h and the step function f _A to obtain the batch function h The incremental processing algorithm A _Δ corresponding to the processing algorithm;

or;

S130. When the batch graph algorithm A is fixed point calculation, judge whether the batch graph algorithm A has a bounded incremental property; when the batch graph algorithm A has a bounded incremental property , then the batch processing algorithm A is transformed into an incremental processing algorithm A _Δ , and the incremental processing algorithm A _Δ has a bounded incremental property.

In the embodiment of the present application, by obtaining the batch processing graph algorithm; when the batch processing graph algorithm is fixed point calculation, the batch processing graph algorithm is obtained from the data structure and logic of the batch processing graph algorithm As a step function for fixed point calculation; according to the data structure and logic of the batch graph algorithm, an initial range function based on the graph update area is generated; the initial range function and the step function are combined to obtain the same value as the original range function the incremental processing algorithm corresponding to the batch processing algorithm; or; when the batch processing graph algorithm is a fixed point calculation, judging whether the batch processing graph algorithm has a bounded incremental property; when the batch processing graph algorithm When the graph algorithm has a bounded incremental property, the batch processing algorithm is converted into an incremental processing algorithm, and the incremental processing algorithm has a bounded incremental property, which can obtain a more efficient method than batch processing recalculation Do incremental calculations.

Next, an automatic increment method of a graph algorithm in this exemplary embodiment will be further described.

As described in the step S110, obtain the batch graph algorithm A;

The batch graph algorithm A (batch algorithms) is defined as follows:

Input graph data G and query Q, the batch processing graph algorithm A answers the query Q on the graph data G, and outputs A(Q, G) as the query result Q(G);

The incremental processing algorithm A _Δ (incremental algorithm) corresponding to the batch graph algorithm A is defined as follows:

Input graph data G, query Q, query result Q(G) and graph data update ΔG, the incremental processing algorithm A _Δ processes the data update ΔG on the graph data G, and outputs A _Δ (Q,G,Q(G ),ΔG) as

The amount of change relative to Q(G), that is:

As described in step S120, when the batch graph algorithm A is fixed point calculation, the batch graph algorithm A is obtained from the data structure and logic of the batch graph algorithm A as a fixed point The calculated step function f _A ; according to the data structure and logic of the batch graph algorithm A, an initial range function h based on the graph update area ΔG is generated; the initial range function h and the step function f _A are combined , to obtain the incremental processing algorithm A _Δ corresponding to the batch processing algorithm.

A batch graph algorithm A, when run on a graph G, builds an auxiliary structure _D _A that expands the graph by the state variables _xi associated with the nodes and edges in the graph G and the part size of the split result Q(G) G, the auxiliary structure D _A records the calculation process and evolves continuously throughout the calculation process. Therefore, the segmentation process of the batch graph algorithm A can be described as a continuous update of the auxiliary structure D _A.

The continuous update of the auxiliary structure D _A is often performed in time order, with

Indicates the state of the auxiliary structure D _A after t iterations; by inputting

and the change value calculated by the update function _f on a specific update region Ht to obtain

details as follows:

The update function f is obtained from the original logic of the batch graph algorithm A; the update area H _t of the t+1 iteration is represented by the state

as input, and generated by the initial range function h of the batch graph algorithm A; the computation continues until

stop, at this time, the

As the segmentation result of Batch Graph Algorithm A.

If a batch graph algorithm A conforms to the above iterative calculation model, it is judged to be a fixed point calculation.

It should be noted that the initial range function h determines the update area by obtaining the information of the previous iteration, that is, the state variables of the auxiliary structure D _A to be updated; the update function f deduces the actual changes of these state variables, for example, decides not Partial assignment of assigned nodes and edges, i.e., the computation process of Batch Graph Algorithm A is guided by changing values at runtime (i.e., change propagation).

Example 1, for a graph growth model that generates two-way edge segmentation, a starting node is selected from the graph, and the graph is grown around an edge-segmented segmented area by breadth-first search (BFS) until Half of the nodes are included, and the rest of the nodes are placed into another edge-segmented split region. As shown in graph G in Figure 2 (only solid edges are considered), w' ₀ can be selected as the starting node, and then v ₁ ,...,v ₁₉ , u' ₁ ,...,u' ₁₉ ,w ' ₀ and w ₀ are put into the V1 part for graph growth, while the rest _of the nodes in G are put into the _V2 part.

The above graph growth model is an iterative batch graph algorithm. Its state variables include the part ID and part size of each node. In each iteration, its update function f takes a set of unallocated vertices, a node to be updated As input, the part ID and corresponding part size of , it assigns part IDs to these vertices and updates their sizes accordingly, and obtains the unassigned neighbor nodes of newly assigned nodes through the initial range function h.

The application of the update function f and the initial range function h can be done in parallel, e.g. to assign different vertices or edges simultaneously in one parallel iteration.

The iterative segmentation algorithms that meet the fixed point calculation include: (1) graph growing algorithm (graph growing), greedy growing algorithm (greedy growing), k-way graph greedy growing algorithm (K-Way Graph Greedy Growing Partitioning, KGGGP) and bubble methods; (2) Neighborhood embedding (NE) and discriminant neighborhood embedding (DNE) applied to vertex segmentation; and (3) Applied to streaming Set Fennel algorithm, High-Degree (are) Replicated First (HDRF), Ginger algorithm, and Greedy algorithm (Greedy); although streaming segmentation algorithms are only developed for insertion, they can still be processed incrementally General update.

The METIS algorithm applied to edge segmentation and the Sheep algorithm applied to vertex segmentation are iterative segmentation algorithms that are not suitable for fixed point calculation, because they will change the topology of the graph during the segmentation process, which exceeds the expressive ability of the iterative calculation model.

If the batch processing algorithm A is fixed point calculation, the batch processing algorithm A is converted into an incremental processing algorithm A _Δ , so that the incremental processing algorithm A _Δ has two characteristics, (1) relative incremental Bounded, (2) preserves the segmentation quality of Batch Graph Algorithm A, as follows:

(1) The relative increment is bounded. Given graph G, graph update area ΔG, balance factor ψ, query result Q(G) generated by batch graph algorithm A running on graph G, and possible auxiliary structure D _{A of batch graph algorithm A} ; Quantity processing algorithm A _Δ calculates the ΔO obtained by updating the region ΔG of the graph, so that

A query result of . Its overhead can be expressed as |CHANGED|=|ΔG|+|ΔO|, in addition, the size of |ΔO| can be expressed as a polynomial of |ΔG|.

(2) Preserve the original segmentation quality. request new query results

Keeping the same balance factor as Q(G), in addition, the incremental processing algorithm A _Δ is required to keep the same constraints on the split size as the batch graph algorithm A. Therefore, if batch graph algorithm A is widely used, the quality of incremental processing algorithm A _Δ is also acceptable to users of batch graph algorithm A.

To derive an efficient incremental processing algorithm A _Δ from a batch graph algorithm A, first determine the fundamental changes associated with the graph update region ΔG, and then by using the update function f and the initial range function h of the batch graph algorithm A to Handle these changes as follows:

(a) Resume iterations. Given the graph update area ΔG and the final state of the batch graph algorithm A after running in batches

The incremental processing algorithm A _Δ first finds (small) regional changes based on the graph update region ΔG, and then in the state

Perform these changes on to get the new state

That is, the segmentation process is resumed in a new iteration. These are known as base changes related to updates. More specifically, the basic change f(H _T ) in the initial new iteration t+1 is computed by the update function f of the batch graph algorithm A, where

is an update region determined by the range function h' revised from the initial range function h of the batch graph algorithm A, as in the batch graph algorithm A, applying the basic change f(H _T ₎ to the state in HT variable.

based on the new state

The initial range function h of the batch graph algorithm A determines another update region H _T+1 for the next new iteration t+2, and adopts the above method to determine the basic change related to H _T+1 ; then, the update function f is applied to H _T+1 . These two steps are iterated in the incremental processing algorithm A _Δ until the update function f and the initial range function h can no longer be used to operate according to the same logic as the batch graph algorithm A to obtain a new final state of this incremental operation

(b) Rebalance. The input graph update region ΔG may overweight some parts of the old edge-segmented (or vertex-segmented) query result Q(G). When this happens, the incremental processing algorithm A _Δ needs to remove a set of nodes (or edges) from each overweight V _i (or E _i ) such that it satisfies the equilibrium constraint, and then uses the same as above (a ) to reassign U _i with the same strategy.

In fact, the incremental processing algorithm _AΔ redistributes some vertices or edges that are either overwritten by the incoming update or picked out for rebalancing. This way helps to refine the old segmentation, because the incremental processing algorithm _AΔ can utilize all the information of the old segmentation. In some cases, the segmentation quality produced this way is even better than re-segmentation with batch graph algorithm A.

Example 2: Continuing from Example 1, for a graph update region ΔG, delete four edges (w ₀ , v ₁ ), (w ₀ , v ₂ ), (w ₁ , v' ₁₈ ) and (w _1, _v'19 ).

Here, the incremental processing algorithm A _Δ directly uses the modified range function h' to obtain an initial new update region, which contains the node set covered by the graph update region ΔG, namely {w' ₀ , v ₁ , v ₂ , w ₁ , v' ₁₈ , v' ₁₉ }; deallocate the above set of nodes, update the size of the corresponding part, and deduce the ID of the candidate part according to the allocation of its neighbors. Next, the incremental processing algorithm A _Δ iteratively reallocates these nodes using the original update of graph growth and the initial range function h (Example 1), placing w ₀ (or w ₁ ) into part V ₂ (or V ₁ ) , and keep the assignments of all other nodes unchanged. That is, the incremental processing algorithm A _Δ only swaps the original assignments of the two nodes.

This is because the incremental processing algorithm A _Δ uses the original logic of the batch graph algorithm _A to continuously update DA, and only limits the changes of the state variables related to the graph update area ΔG and load balancing.

The incremental processing algorithm A _Δ can ensure incremental boundedness when (1) the update function f and the (modified) range functions h and h' can be computed incrementally in polynomial time on the update scale, i.e.,

(or

can be computed from f(d) (or h(d), h'(d)) and Δd without visiting the whole of d; and (2) the overhead of identifying each set _Ui from the overweight part is | _Ui | polynomial.

Specifically, some aggregate functions, such as sum and avg, can be computed incrementally, but the functions that compute eigenvectors in the lineage segmentation method are not.

In fact, the incremental processing algorithm A _Δ only re-evaluates the update function f for regions involving changes, when these functions can be computed incrementally, the magnitude of the change is given by the polynomial of |ΔG| and ∑ _i∈[1,k] |U _i | constraint. If |U _i |≥|ΔG|, i∈[1,k], a new balance constraint can be obtained after rebalancing; and ∑ _i∈[1,k] |U _i | can be obtained by O(|ΔG|) constraint. It should be noted that the rebalancing is performed when the incremental processing algorithm A _Δ starts. Therefore, when the above two conditions hold, the overall overhead and size |ΔO| of the incremental processing algorithm A _Δ is only determined by |ΔG|, that is, the incremental processing algorithm A _Δ is incrementally bounded.

As described in the step S130, when the batch processing graph algorithm A is a fixed point calculation, it is judged whether the batch processing graph algorithm A has a bounded incremental property; when the batch processing graph algorithm A has a When the property of bounded increment is not obtained, the batch processing algorithm A is transformed into an incremental processing algorithm A _Δ , and the incremental processing algorithm A _Δ has the property of bounded increment.

The method for judging that the batch graph algorithm A has a bounded incremental property is: the cost of incremental computation can be calculated by a polynomial function of graph update, segmentation size, and the size of the area affected by the update. Express. It should be noted that this embodiment provides a bounded incremental condition, that is, when the batch graph algorithm A has this property, it can ensure that the incremental processing algorithm obtained by the above automatic incremental method A _Δ is incrementally bounded, i.e. its computational cost is only affected by the extent of graph updates affected by it, and not related to the full graph size. This ensures that the incremental processing algorithm A _Δ does not perform redundant calculations.

In this embodiment, also include:

Determine whether the batch graph algorithm A is AND state

Query results Q(G), graph G and range

A step function related to

iteration of

Wherein, the graph G is an undirected graph; the state

It is the state of the data structure of the batch processing graph algorithm A at the beginning of the preset round (the tth round); the query result Q(G) is obtained after querying the graph G using the batch processing graph algorithm A , the query result Q(G) is composed of the state variables _xi , each of the state variables _xi is associated with a certain point or edge in the graph G, and each of the state Each variable x _i has a corresponding update function for updating the value of the state variable x _i

The update function

input of

is the set of the state variables x _i , each of the state variables x _i corresponds to a logic judgment statement

Satisfied every time using the update function

After updating the state variable x _i , the logic judgment statement

is true, and for all the final converged fixed points, all the logical judgment statements

all true; the range

In order to all correspond to the logic judgment statement when the preset round (the tth round) starts

The state variable x _i that is not;

The step function f _A is used in each round of iterations in the range

The input corresponding to the state variable x _i is executed on all the state variables x _i contained in

Iterate to all the logic judgment statements

is true, the range

for

stop.

If the batch graph algorithm A is the same as the state

The query result Q(G), the graph G and the range

A step function related to

iteration, it is determined that the batch graph algorithm A is fixed point calculation.

In this embodiment, the step of generating the initial range function h based on the graph update area ΔG according to the data structure and logic of the batch graph algorithm A includes:

obtain the input that determines the state variable x _i in the fixed point state

A subset of , as the anchor set of the state variable _xi

According to the anchor set

Generate a directed acyclic graph, the directed acyclic graph contains the topological partial order relationship < _C of each point in the graph G in the fixed point state, and the topological partial order relationship < _C is used to guide the batch processing Change propagation of graph algorithm A;

The initial range function h based on the graph update region ΔG is generated according to the directed acyclic graph.

Specifically, the initial range function h can be generated in the following manner:

(1) Perform change propagation. Since each of the state variables x _i uses its corresponding update function

is updated, so the value of the state variable _xi depends on the update function

The input of

And usually ultimately the state variable _xi only depends on the input

A subset of , but not all of , therefore, record the input that determines the state variable _xi in a fixed-point state

A subset of , as the anchor set of the state variable _xi

According to the anchor set

Build a directed acyclic graph, the directed acyclic graph is used to represent the topological partial order relationship < _C of each point in the graph G in the fixed point state; change propagation is along the direction of the directed acyclic graph Propagation of dependencies;

(2) Fixed point adjustment. An implementation of the initial range function h is given below:

Input: The fixed point state

and the graph update area ΔG;

output: the initial range

and one for the updated graph

Feasible initial state

Collect all the state variables _xi covered by the graph update region ΔG into the initial range

, the initial state

initialized to

Initialize the priority queue que, which contains all the initial ranges in the priority queue que

The priority of the state variable x _i in is according to the partial order relationship of the topological partial order relationship <_C;

In this embodiment, after the step of combining the initial range function h and the step function f _A to obtain the incremental processing algorithm A _Δ corresponding to the batch processing algorithm A, further includes :

Obtaining the query result Q(G) and the update area ΔG of the graph G;

Using the initial range function h, the fixed point state of the query result Q(G)

Modified to for the updated figure

Feasible initial state

and the initial state

initial range on

Use the step function f _A to convert the initial state

and the initial scope

Iterate to new fixed points to obtain the updated graph

query results for

In this embodiment, also include:

When the batch graph algorithm A does not have a bounded incremental property, determine whether the batch graph algorithm A has a weakly incremental property;

When the batch graph algorithm A has a weak incremental property, then the step function f _A and the state of the batch graph algorithm A

modifying, so that the batch processing graph algorithm A has a bounded incremental property; transforming the batch processing algorithm A into an incremental processing algorithm A _Δ , and the incremental processing algorithm A _Δ has a bounded incremental property .

It should be noted that this embodiment provides a state for the batch processing algorithm A

and the modification method of the step function f _A , so that after the modification method is applied to a class of weakly incremental algorithms that do not have the bounded incremental property, they can all have the bounded incremental property, thereby being able to into the corresponding incremental processing algorithm A _Δ .

In this embodiment, the step of converting the batch processing algorithm A into an incremental processing algorithm A _Δ includes:

Obtaining the step function f _{A of the batch graph algorithm A as a fixed point calculation from the data structure and logic of the batch graph algorithm A} ;

Generate an initial range function h based on the graph update area ΔG according to the data structure and logic of the batch graph algorithm A;

The initial range function h and the step function f _A are combined to obtain the incremental processing algorithm A _Δ corresponding to the batch processing algorithm.

In this embodiment, the batch graph algorithm A includes a single-source shortest path algorithm (Single Source Shortest Path, SSSP), a weakly connected component algorithm (Weakly Connected Component, WCC), a depth-first search algorithm (DepthFirst Search, DFS), Any one of Local Clustering Coefficient (LCC) and Graph Simulation.

As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and for related parts, please refer to the part of the description of the method embodiment.

Referring to FIG. 3 , it shows an automatic incrementing device for a graph algorithm provided by an embodiment of the present application, including:

An acquisition module 210, configured to acquire a batch graph algorithm A;

The first processing module 220 is configured to obtain the batch graph algorithm A as a fixed point from the data structure and logic of the batch graph algorithm A when the batch graph algorithm A is a fixed point calculation The calculated step function f _A ; according to the data structure and logic of the batch graph algorithm A, an initial range function h based on the graph update area ΔG is generated; the initial range function h and the step function f _A are combined , to obtain the incremental processing algorithm A _Δ corresponding to the batch processing algorithm;

or;

The second processing module 230 is used to judge whether the batch processing graph algorithm A has a bounded incremental property when the batch processing graph algorithm A is a fixed point calculation; when the batch processing graph algorithm A has a bounded incremental property When the property of bounded increment is not obtained, the batch processing algorithm A is transformed into an incremental processing algorithm A _Δ , and the incremental processing algorithm A _Δ has the property of bounded increment.

In an embodiment of the present application, the first processing module 220 includes:

An anchor set acquisition submodule, used to acquire the input that determines the state variable x _i in the fixed point state

A subset of , as the anchor set of the state variable _xi

Directed acyclic graph generation sub-module for according to the anchor set

The initial range function generating submodule is configured to generate the initial range function h based on the graph update area ΔG according to the directed acyclic graph.

In this embodiment, the second processing module 230 includes:

The second processing submodule is used to determine whether the batch graph algorithm A has a weakly incremental property when the batch graph algorithm A does not have a bounded incremental property;

In this embodiment, also include:

The third processing module is used to obtain the query result Q(G) and the update area ΔG of the graph G; using the initial range function h, the fixed point state of the query result Q(G)

Modified to for the updated figure

Feasible initial state

and the initial state

initial range on

Use the step function f _A to convert the initial state

and the initial scope

Iterate to new fixed points to obtain the updated graph

query results for

Referring to FIG. 4 , it shows a computer device for automatic incrementation of a graph algorithm of the present application, which may specifically include the following:

The above-mentioned computer device 12 is expressed in the form of a general-purpose computing device. The components of the computer device 12 may include, but are not limited to: one or more processors or processing units 16, memory 28, and different system components (including memory 28 and processing unit 16) connected to each other. bus 18.

The bus 18 represents one or more of several types of bus 18 structures, including a memory bus 18 or memory controller, a peripheral bus 18, an accelerated graphics port, a processor, or a bureau using any of a variety of bus 18 structures. domain bus 18. By way of example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus 18, the Micro Channel Architecture (MAC) bus 18, the Enhanced ISA bus 18, the Audio Video Electronics Standards Association (VESA) local bus 18, and Peripheral Component Interconnect (PCI) bus 18 .

Computer device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by computer device 12 and include both volatile and nonvolatile media, removable and non-removable media.

Memory 28 may include computer system readable media in the form of volatile memory, such as random access memory 30 and/or cache memory 32 . The computer device 12 may further include other removable/non-removable, volatile/nonvolatile computer system storage media. By way of example only, storage system 34 may be used to read from and write to non-removable, non-volatile magnetic media (commonly referred to as a "hard drive"). Although not shown in FIG. 4, a disk drive for reading and writing to removable non-volatile disks (such as "floppy disks") may be provided, as well as for removable non-volatile optical disks (such as CD-ROM, DVD-ROM or other optical media) CD-ROM drive. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. The memory may include at least one program product having a set (eg, at least one) of program modules 42 configured to perform the functions of various embodiments of the present application.

program/utility 40 having a set (at least one) of program modules 42, such as may be stored in memory, such program modules 42 including - but not limited to - an operating system, one or more application programs, other program modules 42 and program data, each or some combination of these examples may include the implementation of the network environment. The program modules 42 generally perform the functions and/or methods of the embodiments described herein.

The computer device 12 may also communicate with one or more external devices 14 (e.g., a keyboard, pointing device, display 24, camera, etc.), and with one or more devices that enable an operator to interact with the computer device 12, and and/or communicate with any device (eg, network card, modem, etc.) that enables the computing device 12 to communicate with one or more other computing devices. Such communication may occur through I/O interface 22 . Also, computer device 12 may communicate with one or more networks (eg, local area network (LAN)), wide area network (WAN) and/or public networks (eg, the Internet) via network adapter 20 . As shown in FIG. 4 , network adapter 20 communicates with other modules of computer device 12 via bus 18 . It should be appreciated that although not shown in FIG. 4 , other hardware and/or software modules may be used in conjunction with computer device 12, including but not limited to: microcode, device drivers, redundant processing units 16, external disk drive arrays, RAID systems, Tape drives and data backup storage systems 34 and the like.

The processing unit 16 executes various functional applications and data processing by running the programs stored in the memory 28 , for example, implementing an automatic increment method of a graph algorithm provided by the embodiment of the present application.

That is, when the above-mentioned processing unit 16 executes the above-mentioned program, it realizes: obtaining a batch processing graph algorithm A; when the batch processing graph algorithm A is fixed point calculation, then from the data structure and logic of the batch processing graph algorithm A Obtain the step function f _A calculated by the batch graph algorithm A as a fixed point; generate an initial range function h based on the graph update area ΔG according to the data structure and logic of the batch graph algorithm A; set the initial range function h and the step function f _A are combined to obtain the incremental processing algorithm A _Δ corresponding to the batch processing algorithm; or; when the batch processing graph algorithm A is a fixed point calculation, determine the Whether the batch processing graph algorithm A has a bounded incremental property; when the batch processing graph algorithm A has a bounded incremental property, then the batch processing algorithm A is converted into an incremental processing algorithm A _Δ , so The incremental processing algorithm A _Δ has the property of bounded incrementalization.

In one embodiment of the present application, there is also provided a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, an automatic increment of a graph algorithm as provided in all embodiments of the present application is realized method.

That is to say, when the program is executed by the processor, it is realized that the batch processing graph algorithm A is obtained; when the batch processing graph algorithm A is fixed point calculation, it is obtained from the data structure and logic of the batch processing graph algorithm A The batch graph algorithm A is used as the step function f _A calculated by the fixed point; according to the data structure and logic of the batch graph algorithm A, an initial range function h based on the graph update area ΔG is generated; the initial range function h and the step function f _A are combined to obtain the incremental processing algorithm A _Δ corresponding to the batch processing algorithm; or; when the batch processing graph algorithm A is fixed point calculation, determine the Whether the batch processing graph algorithm A has a bounded incremental property; when the batch processing graph algorithm A has a bounded incremental property, then the batch processing algorithm A is converted into an incremental processing algorithm A _Δ , the Incremental processing algorithm A _Δ has bounded incremental properties.

Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (non-exhaustive list) of computer readable storage media include: electrical connections with one or more leads, portable computer disks, hard disks, random access memory (RAM), read only memory (ROM), Erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination of the above. In this document, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

A computer readable signal medium may include a data signal carrying computer readable program code in baseband or as part of a carrier wave. Such propagated data signals may take many forms, including - but not limited to - electromagnetic signals, optical signals, or any suitable combination of the foregoing. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. .

Computer program codes for performing the operations of the present application may be written in one or more programming languages or combinations thereof, including object-oriented programming languages such as Java, Smalltalk, C++, and conventional Procedural programming language - such as "C" or a similar programming language. The program code may execute entirely on the operator computer, partly on the operator computer, as a stand-alone software package, partly on the operator computer and partly on a remote computer or entirely on the remote computer or server . In cases involving a remote computer, the remote computer can be connected to the operator computer via any kind of network, including a local area network (LAN) or wide area network (WAN), or it can be connected to an external computer (e.g. using an Internet service provider to connect via the Internet). Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other.

While the preferred embodiments of the embodiments of the present application have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once the basic inventive concept is understood. Therefore, the appended claims are intended to be interpreted to cover the preferred embodiment and all changes and modifications that fall within the scope of the embodiments of the application.

Finally, it should also be noted that in this text, relational terms such as first and second etc. are only used to distinguish one entity or operation from another, and do not necessarily require or imply that these entities or operations, any such actual relationship or order exists. Furthermore, the term "comprises", "comprises" or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article, or terminal equipment comprising a set of elements includes not only those elements, but also includes elements not expressly listed. other elements identified, or also include elements inherent in such a process, method, article, or end-equipment. Without further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article or terminal device comprising said element.

The above is a detailed introduction to the automatic increment method, device, equipment and storage medium of a graph algorithm provided by this application. In this paper, specific examples are used to illustrate the principle and implementation of this application. The above examples The description is only used to help understand the method of the present application and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation and application scope. In summary, As stated above, the contents of this specification should not be construed as limiting the application.

Claims

An automatic incremental method for a graph algorithm, characterized in that it includes:

Get the batch graph algorithm;

When the batch processing graph algorithm is a fixed point calculation, the batch processing graph algorithm is obtained from the data structure and logic of the batch processing graph algorithm as a step function of the fixed point calculation; according to the batch processing The data structure and logic of the graph algorithm generate an initial range function based on the graph update area; combine the initial range function and the step function to obtain an incremental processing algorithm corresponding to the batch processing algorithm;

or;

When the batch processing graph algorithm is a fixed point calculation, it is judged whether the batch processing graph algorithm has a bounded incremental property; when the batch processing graph algorithm has a bounded incremental property, then the The batch processing algorithm is transformed into an incremental processing algorithm, which has a bounded incremental property.
The automatic increment method according to claim 1, further comprising:

Judging whether the batch processing graph algorithm is an iteration of a step function related to the graph, state, query result and range; wherein, the graph is an undirected graph; the state is the data structure of the batch processing graph algorithm The state at the beginning of the preset round; the query result is the query result obtained after using the batch graph algorithm to query the graph, the query result is composed of the state variables, and each of the state variables is Associated with a certain point or edge in the graph, each of the state variables has a corresponding update function for updating the value of the state variable, and the input of the update function is a set of the state variables , each of the state variables corresponds to a logic judgment statement, satisfying that after each update function is used to update the state variable, the logic judgment statement is true, and for the final fixed point state, all the logic The judgment statement is all true; the range includes the state variables that all correspond to the logic judgment statement being negated when the preset round starts;

If the batch graph algorithm is an iteration of a step function related to the state, the query result, the graph, and the range, then the batch graph algorithm is determined to be a fixed point computation.
The automatic increment method according to claim 2, wherein the step of generating an initial range function based on a graph update region according to the data structure and logic of the batch graph algorithm comprises:

Obtaining a subset of the input of the update function in a fixed point state as an anchor set of the state variable;

Generate a directed acyclic graph according to the anchor set, the directed acyclic graph includes the topological partial order relationship of each point in the graph in the fixed point state, and the topological partial order relationship is used to guide the batch handles change propagation for graph algorithms;

The initial range function based on the graph update region is generated from the directed acyclic graph.
The automatic incrementalization method according to claim 3, wherein the initial range function and the step function are combined to obtain the incremental processing algorithm corresponding to the batch processing algorithm After the steps, also include:

Obtaining the query result and the update area of the graph;

modifying the fixed point state of the query result to an initial state feasible for the updated graph and an initial range on the initial state using the initial range function;

The step function is used to iterate the initial state and the initial range to a new fixed point to obtain a query result of the updated graph.
The automatic increment method according to claim 2, further comprising:

When the batch graph algorithm does not have a bounded incremental property, determine whether the batch graph algorithm has a weakly incremental property;

When the batch processing graph algorithm has a weakly incremental property, the step function and the state of the batch processing graph algorithm are modified so that the batch processing graph algorithm has bounded incrementalization property; converting the batch processing algorithm into an incremental processing algorithm, and the incremental processing algorithm has a bounded incremental property.
The automatic incremental method according to claim 1, wherein the step of converting the batch processing algorithm into an incremental processing algorithm comprises:

deriving the batch graph algorithm as a step function for fixed point computation from the batch graph algorithm's data structure and logic;

Generate an initial range function based on the graph update region according to the data structure and logic of the batch graph algorithm;

Combining the initial range function and the step function to obtain an incremental processing algorithm corresponding to the batch processing algorithm.
The automatic incrementalization method according to claim 1, wherein the batch graph algorithm includes a weakly connected component algorithm, a single-source shortest path algorithm, a depth-first search algorithm, a local clustering coefficient algorithm, and a graph simulation algorithm. any of the
An automatic incrementalization device for a graph algorithm, characterized in that it includes:

Obtaining a module for obtaining a batch graph algorithm;

The first processing module is used to obtain the step of the batch graph algorithm as a fixed point calculation from the data structure and logic of the batch graph algorithm when the batch graph algorithm is a fixed point calculation function; generate an initial range function based on the graph update region according to the data structure and logic of the batch processing graph algorithm; combine the initial range function and the step function to obtain an increment corresponding to the batch processing algorithm processing algorithm;

or;

The second processing module is used to determine whether the batch graph algorithm has a bounded incremental property when the batch graph algorithm is a fixed point calculation; when the batch graph algorithm has a bounded incremental property When the property is , the batch processing algorithm is transformed into an incremental processing algorithm, and the incremental processing algorithm has a bounded incremental property.
A device, characterized in that it comprises a processor, a memory, and a computer program stored on the memory and capable of running on the processor, when the computer program is executed by the processor, it implements claims 1 to 1. The method described in any one of 7.
A computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.