CN101458716A - Shortcut searching method between nodes in chart - Google Patents
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- CN101458716A CN101458716A CNA2008102474859A CN200810247485A CN101458716A CN 101458716 A CN101458716 A CN 101458716A CN A2008102474859 A CNA2008102474859 A CN A2008102474859A CN 200810247485 A CN200810247485 A CN 200810247485A CN 101458716 A CN101458716 A CN 101458716A
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Abstract
The invention discloses a method for looking up a shortest path between nodes in a picture, the method comprises two steps: firstly calculating the shortest paths of all nodes to implement coding; secondly implementing the shortest path discovery by using the calculated node to code in advance. The invention can improve the path discovery executing efficiency by using the calculated and selected path in advance and less space expense, and can greatly improve the lookup time of the shortest path between nodes.
Description
Technical field
The present invention relates to the diagram data management domain, particularly relate in a kind of diagram data the lookup method of shortest path between node.
Background technology
Along with the fast development of computer technology, the diagram data administrative skill has also obtained fast development.For the ease of the computing machine fast processing, often that some are concrete technical matters is abstract to be diagram data, for example field of traffic, with the station abstract be node, with the traffic route between the station abstract be the limit, like this, just the route problem between the station is converted into diagram data.
In the diagram data management process, find that the shortest path of two nodes is basic operations.Traditional algorithm can be found the shortest path of two nodes, but calculation cost is very high.With the dijkstra's algorithm is example, and its calculation cost rises along with number of nodes becomes the square number magnitude with parameter, and under the bigger situation of number of nodes or limit quantity, the performance of dynamic operation is difficult to satisfy user's requirement.In order to reduce the cost of the time of running, a kind of feasible scheme is to preserve shortest path information in advance.Adopt fundamental method, if according to node to preserving, then need n
2Right, each shortest path needs n according under the worst situation, so the preservation of whole shortest path information needs n
3When node data was more, this cost was difficult to bear.Another replacement scheme is the shortest path tree that certain node of storage sets out, and then the space cost drops to n
2But the space cost is still very high.
Summary of the invention
The purpose of this invention is to provide in a kind of diagram data the lookup method of shortest path between node, a kind of method of searching shortest path between node fast particularly is provided.
For achieving the above object, technical scheme of the present invention provides among a kind of figure the lookup method of shortest path between node, said method comprising the steps of:
S1 calculates all internodal shortest paths among the figure of source, and encodes, and internodal maximum hop count k is set in cataloged procedure;
S2, from the figure of source, determine to search first of shortest path with second point, according to above-mentioned node, coding and maximum hop count k, obtain described first shortest path with point to point.
Wherein, encode among the described step S1 and be meant: at any one the node n among the figure of source, have two set inNodes and outNodes, in the inNodes set, data mode is (m, cost), record node m is to the shortest path cost of n, and in the outNodes set, data mode is (m, cost), record node n is to the shortest path cost of m.
Wherein, step S1 specifically may further comprise the steps:
S1-1, for any one node n among the figure of source, one of structure is the shortest path tree spt (n) of root node with n in the figure of source; In shortest path tree, from n to tree the path of any one node m be exactly among the figure n to the shortest path of m;
S1-2, according to the k value of input, the outNodes set of location n in spt (n), this set is labeled as Nodes1, is described as the outNodes common factor that Node1={a|a belongs to middle node set of spt (n) and n };
S1-3, in the Node1 set, obtain node n1, obtain the common factor between the outNodes of subtree that n1 is a root node and n1, be labeled as Node2, Node2={a|a is in subtree (n1) and n1.outNodes, n1 is at Node1}, and wherein subtree (n1) expression is the subtree of root node with n1;
S1-4 obtains node n2 in Node2 set, with mark Node2 set identical method mark Node3, Node4 ..., till reaching given k threshold value;
S1-5 preserves above-mentioned coding result.
Wherein, after step S1-5, further comprising the steps of:
S1-6 judges whether any node m in the described shortest path tree passes through coding, if then circulation step S1-6 passes through coding up to all nodes; If not, then encode.
Wherein, the step of encoding among the step S1-6 comprises:
S1-7 determines the path from first to node m in the described shortest path tree;
S1-8 is divided into the k equal portions with this path, determines each separation;
S1-9 adds each separation p in the outNode set of previous separation of p, and a separation before the p is added in the inNode set of p.
Wherein, step S2 specifically may further comprise the steps:
S3-1 judges whether k is even number, if then change step S3-2, otherwise change step S3-6;
S3-2, since first, according to first outNode set, expansion obtains the set Node1 of first child node, again according to the outNode set of first child node, obtains the child node set Node2 of child node.Cost adds up in the expansion process, and first node of mark is to the bee-line of this node; And the like, expansion
Inferior, obtain gathering NodeR, NodeS be set be set Node1, Node2 ..., the union of NodeR;
S3-3, from described second, inNode set according to second, expansion obtains the set Node1 ' of second child node, again according to the inNode set of second child node, obtain that cost adds up in the child node set Node2 ' expansion process of child node, this node of mark is to the bee-line of Section Point; , and the like, expansion
Inferior, obtain gathering NodeR '; Set NodeS ' be set be set Node1 ', Node2 ' ..., the union of NodeR ';
S3-4 obtains the common factor of set NodeS and set NodeS ', and obtains a node m therein, adds up to m from first and goes up m to the second cost sum minimum, and m is first o'clock to the second o'clock intermediate node in the shortest path;
S3-5 utilizes the method for recurrence, obtains at first to the shortest path of m and m to the second shortest path;
S3-6, since first, outNode set according to first, expansion obtains the set Node1 of first child node, again according to the outNode set of first child node, obtain that cost adds up in the child node set Node2. expansion process of child node, first node of mark is to the bee-line of this node, and the like, expansion
Inferior, obtain gathering NodeO, set NodeP be set be set Node1, Node2 ..., the union of NodeO;
S3-7, from described second, inNode set according to second, expansion obtains second the set Node1 ' of child node, again according to the inNode set of second child node, obtains the child node set Node2 ' of child node, cost adds up in the expansion process, the bee-line of this node to the second of mark node, and the like, expansion
Inferior, obtain gathering NodeO '; NodeP ' be set be set Node1 ', Node2 ' ..., the union of NodeO ';
S3-8 gets a less set of set NodeP and the middle number of nodes of NodeP ' and expands once again, obtains gathering NodeQ;
S3-9, obtain set that does not have expansion among set NodeP and the NodeP ' and the common factor of gathering NodeQ, and in this common factor, obtain a node m, and adding up to m from first and go up m to the second cost sum minimum, m is first o'clock to the second o'clock intermediate node in the shortest path;
S3-10 utilizes the method for recurrence, obtains at first to the shortest path of m and m to the second shortest path.
Wherein, further comprising the steps of after step S2:
S3 preserves shortest path information, nodal information, coded message and maximum hop count k information between described first and second.
Technique scheme has following advantage: utilization of the present invention is calculated in advance and is selected the path, at first in the path of calculating, search, when the path is not searched in the path of calculating, carry out new searching again, and preserve corresponding results and coding result, so that search use later on, saved the time of searching greatly, improve the execution efficient of path discovery by less space cost, improved searching the time of shortest path between node greatly.
Description of drawings
Fig. 1 is the process flow diagram of the lookup method of shortest path between node among a kind of figure of the embodiment of the invention;
Fig. 2 is the structural representation of a kind of shortest path number of the embodiment of the invention;
Fig. 3 is the structural representation of the another kind of shortest path number of the embodiment of the invention.
Embodiment
Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.Following examples are used to illustrate the present invention, but are not used for limiting the scope of the invention.
The large amount of complex data that occur as road graticule, social networks, biomolecule etc., can abstractly be diagram data at present.A kind of important operation on the diagram data is exactly the shortest path of finding between two nodes.Along with the increase of diagram data scale, the efficient of traditional path discovery algorithm can not meet the demands.In order to improve the path discovery efficiency of the time of running, this patent has proposed node shortest path index technology, by the precalculated node relationships of memory limited, improves the discovery efficient of shortest path between 2 of times of running.By way of example, in social networks, participating in social personnel abstract is a node, and the contact between the personnel is abstract to be a limit.This patent can be found two interpersonal relations between the personnel fast.In field of traffic, this patent can be found two paths between the station.Aspect mobile node network route, the present invention can find two routed paths between the node.With respect to the traditional shortest path algorithm of direct use, utilization of the present invention is calculated in advance and is selected the path, improves the execution efficient of path discovery by less space cost.
The lookup method of shortest path between node was divided into for two steps among the figure of present embodiment, and the first step is an off-line, was exactly the shortest path that calculates all nodes in advance, realized coding; Second one is online, is exactly to utilize to calculate good nodes encoding in advance, realizes the shortest path discovery.Specifically may further comprise the steps:
S1 calculates all internodal shortest paths among the figure of source, and encodes, and internodal maximum hop count k is set in cataloged procedure; Maximum hop count k is meant that jumping the back from first through k arrives second point, that is to say, if maximum hop count k is 3, jumps the back from first o'clock through 3 and arrives second point, promptly has 2 intermediate nodes between first and second.Maximum hop count k is the demand setting of client according to oneself, and when client's data processing equipment computing power is stronger, and the client wishes to obtain one more accurately during information, and less maximum hop count k can be set, otherwise, bigger maximum hop count k is set.
S2, from the figure of source, determine to search first of shortest path with second point, according to above-mentioned node, coding and maximum hop count k, obtain described first shortest path with point to point.
S3 preserves shortest path information, nodal information, coded message and maximum hop count k information between described first and second.
Wherein, encode among the step S1 and be meant: at any one the node n among the figure of source, have two set inNodes and outNodes, in the inNodes set, data mode is (m, cost), record node m is to the shortest path cost of n, and in the outNodes set, data mode is (m, cost), record node n is to the shortest path cost of m.
Step S1 specifically may further comprise the steps:
S1-1, for any one node n among the figure of source, one of structure is the shortest path tree spt (n) of root node with n in the figure of source; In shortest path tree, from n to tree the path of any one node m be exactly among the figure n to the shortest path of m;
S1-2, according to the k value of input, the outNodes set of location n in spt (n), this set is labeled as Nodes1, is described as the outNodes common factor that Node1={a|a belongs to middle node set of spt (n) and n };
S1-3, in the Node1 set, obtain node n1, obtain the common factor between the outNodes of subtree that n1 is a root node and n1, be labeled as Node2, Node2={a|a is in subtree (n1) and n1.outNodes, n1 is at Node1}, and wherein subtree (n1) expression is the subtree of root node with n1;
S1-4 obtains node n2 in Node2 set, with mark Node2 set identical method mark Node3, Node4 ..., till reaching given k threshold value; Above-mentioned steps specifically, be exactly mark Node1, Node2 ..., the jumping figure among the Nodek on the node.
S1-5 preserves above-mentioned coding result.
After step S1-5, further comprising the steps of:
S1-6 judges that any node m in the described shortest path tree whether through coding, that is to say, judges the jumping figure mark mistake whether on the m point, if then circulation step S1-6 passes through coding up to all nodes; If not, then encode.The step of coding specifically comprises:
S1-7 determines the path from first to node m in the described shortest path tree;
S1-8 is divided into the k equal portions with this path, determines each separation;
S1-9 adds each separation p in the outNode set of previous separation of p, and a separation before the p is added in the inNode set of p.
Wherein, step S2 specifically may further comprise the steps:
S3-1 judges whether k is even number, if then change step S3-2, otherwise change step S3-6;
S3-2, since first, according to first outNode set, expansion obtains the set Node1 of first child node, again according to the outNode set of first child node, obtains the child node set Node2 of child node.Cost adds up in the expansion process, and first node of mark is to the bee-line of this node; And the like, expansion
Inferior, obtain gathering NodeR, NodeS be set be set Node1, Node2 ..., the union of NodeR;
S3-3, from described second, inNode set according to second, expansion obtains the set Node1 ' of second child node, again according to the inNode set of second child node, obtain that cost adds up in the child node set Node2 ' expansion process of child node, this node of mark is to the bee-line of Section Point; , and the like, expansion
Inferior, obtain gathering NodeR '; Set NodeS ' be set be set Node1 ', Node2 ' ..., the union of NodeR ';
S3-4 obtains the common factor of set NodeS and set NodeS ', and obtains a node m therein, adds up to m from first and goes up m to the second cost sum minimum, and m is first o'clock to the second o'clock intermediate node in the shortest path;
S3-5 utilizes the method for recurrence, obtains at first to the shortest path of m and m to the second shortest path;
S3-6, since first, outNode set according to first, expansion obtains the set Node1 of first child node, again according to the outNode set of first child node, obtain that cost adds up in the child node set Node2. expansion process of child node, first node of mark is to the bee-line of this node, and the like, expansion
Inferior, obtain gathering NodeO, set NodeP be set be set Node1, Node2 ..., the union of NodeO;
S3-7, from described second, inNode set according to second, expansion obtains second the set Node1 ' of child node, again according to the inNode set of second child node, obtains the child node set Node2 ' of child node, cost adds up in the expansion process, the bee-line of this node to the second of mark node, and the like, expansion
Inferior, obtain gathering NodeO '; NodeP ' be set be set Node1 ', Node2 ' ..., the union of NodeO ';
S3-8 gets a less set of set NodeP and the middle number of nodes of NodeP ' and expands once again, obtains gathering NodeQ;
S3-9, obtain set that does not have expansion among set NodeP and the NodeP ' and the common factor of gathering NodeQ, and in this common factor, obtain a node m, and adding up to m from first and go up m to the second cost sum minimum, m is first o'clock to the second o'clock intermediate node in the shortest path;
S3-10 utilizes the method for recurrence, obtains at first to the shortest path of m and m to the second shortest path.
Entire method is divided into two steps, and one is the index construction phase, and one is to utilize index information to find the stage of shortest path.Describe with instantiation below.
(N, E), maximum hop count k at each the node n among the figure, has two set inNodes and outNodes to given figure G=.In the inNodes set, data mode is that (m cost), writes down the shortest path cost of node m to n, and cost is meant from node m to the path the n.In the outNodes set, data mode is that (m cost), writes down the shortest path cost of node n to m, and same, cost is meant from node n to the path the m.
For any one node n among the figure, we find algorithm according to present shortest path, and constructing one in the drawings is the shortest path tree spt (n) of root node with n.In this tree, from n to tree the path of other nodes m, be exactly the shortest path from n to m in the figure G of source.
We begin to produce the shortest path coding that the n node is the root node in shortest path tree, mainly are divided into two parts, initialization section and coded portion:
Initialization section comprises: according to the k value of input, we finish following operation: the outNodes set of location n in spt (n), this set is labeled as Nodes1, perhaps be described as Node1={a|a and belong to node set and n.outNodes common factor among the spt (n) }, in the Node1 set, obtain node n1, we find that n1 is the common factor between the outNodes of the subtree of root node and n1, Node2={a|a is in subtree (n1) and n1.outNodes, n1 is at Node1}, and wherein subtree (n1) expression is the subtree of root node with n1.
Similar and the Node2 of the definition of Node3, we continue mark, till reaching given k threshold value.Coded portion comprises: as shown in Figure 2, suppose that 1 outNode set comprises 5 and 8,8 outNodes set and comprises b and c.Our structure is the shortest path tree of root node with 1, begins coding.Because 1 outNodes set comprises 5 and 8,8 outNodes set and comprises b and c, this means 5,8, face code embodies before b, the c, if k=3 then need not 58bc is encoded.But remaining node still needs coding, preserves the 1 shortest path information to other nodes.
Coded portion:, determine that (n, m), (n divides the k equal portions according to subscript in m) to n, determines each separation at path path to the path path of m for the node m that is not labeled among the shortest path tree spt (n).For separation s, suppose that its relative position is i, if s is not labeled, perhaps s is labeled, but the mark of s greater than i, then s is labeled as i, simultaneously, s is increased to path[i-1] outNodes in, with path[i-1] be increased among the inNodes of s.If s is labeled, the mark of s then need not to increase s in coding less than i simultaneously.Repeated treatments finishes up to all vertex ticks.
Fig. 3 represents the shortest path from node1 to node m, supposes k=3, and then whole sequence is divided into 3 parts, and separation comprises 1, a, 3, m; We need guarantee to find m within 3 of a jumps.Coding result is as follows:
A is increased to 1 outNodes, and 1 is increased to the inNodes of a;
A is increased to 3 inNodes, and 3 are increased to the outNodes of a;
3 are increased to the inNodes of m, and m is increased to 3 outNodes.
Introduce given node and its inNodes below, the data of outNodes are found the route method between any 2.For example: given node n and node m, we begin to utilize inNodes and outNodes to find the path.
From the n node, according to outNodes, expansion [k/2] is inferior, obtains the Node1 node set;
From the m node, according to inNodes, expansion [k/2] is inferior, obtains the Node2 node set.
If k is an even number, expansion stops, if k is an odd number, the less set of number of nodes continues expansion once among selection Node1 and the Node2.Obtain intermediate node set Mid={a|a in node1, a is at node2, and (n, cost+ a) (a, cost minimum m) } in.If have only a node among the Mid, then we utilize the method for recurrence, continue to find the path of n to the path of a and a to m.If there are a plurality of nodes among the Mid, then we utilize the method for recurrence according to the ordering of n to the distance of these nodes, find the shortest path of each node space.
For example, as shown in Figure 3, find 1 to m shortest path, we obtain the Node1 set from 1 outNodes, comprise a; We obtain the Node2 set from the inNodes of m, comprise 3; We further expand Node1, join among the Node1 3.The total data of Node1 and Node2 are 3, calculation cost, and add up 3 to m cost of 1 to 3 cost, minimum in whole mid set.So we determine that 3 is 1 intermediate nodes to the m shortest path.Our profit uses the same method and obtains path between 1 to 3 and the path between 3 to m.
The above only is a preferred implementation of the present invention; should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the technology of the present invention principle; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.
Claims (7)
1, the lookup method of shortest path between node among a kind of figure is characterized in that, said method comprising the steps of:
S1 calculates all internodal shortest paths among the figure of source, and encodes, and internodal maximum hop count k is set in cataloged procedure;
S2, from the figure of source, determine to search first of shortest path with second point, according to above-mentioned node, coding and maximum hop count k, obtain described first shortest path with point to point.
2, the lookup method of shortest path between node among the figure as claimed in claim 1, it is characterized in that encoding among the described step S1 is meant:, have two set inNodes and outNodes at any one the node n among the figure of source, in the inNodes set, data mode is that (m cost), writes down the shortest path cost of node m to n, in the outNodes set, data mode is that (m, cost), record node n is to the shortest path cost of m.
3, the lookup method of shortest path between node among the figure as claimed in claim 2 is characterized in that step S1 specifically may further comprise the steps:
S1-1, for any one node n among the figure of source, one of structure is the shortest path tree spt (n) of root node with n in the figure of source; In shortest path tree, from n to tree the path of any one node m be exactly among the figure n to the shortest path of m;
S1-2, according to the k value of input, the outNodes set of location n in spt (n), this set is labeled as Nodes1, is described as the outNodes common factor that Node1={a|a belongs to middle node set of spt (n) and n };
S1-3, in the Node1 set, obtain node n1, obtain the common factor between the outNodes of subtree that n1 is a root node and n1, be labeled as Node2, Node2={a|a is in subtree (n1) and n1.outNodes, n1 is at Node1}, and wherein subtree (n1) expression is the subtree of root node with n1;
S1-4 obtains node n2 in Node2 set, with mark Node2 set identical method mark Node3, Node4 ..., till reaching given k threshold value;
S1-5 preserves above-mentioned coding result.
4, the lookup method of shortest path between node among the figure as claimed in claim 3 is characterized in that, and is after step S1-5, further comprising the steps of:
S1-6 judges whether any node m in the described shortest path tree passes through coding, if not, then encodes.
5, the lookup method of shortest path between node among the figure as claimed in claim 4 is characterized in that the step of encoding among the step S1-6 comprises:
S1-7 determines the path from first to node m in the described shortest path tree;
S1-8 is divided into the k equal portions with this path, determines each separation;
S1-9 adds each separation p in the outNode set of previous separation of p, and a separation before the p is added in the inNode set of p.
6, the lookup method of shortest path between node among the figure as claimed in claim 5 is characterized in that step S2 specifically may further comprise the steps:
S3-1 judges whether k is even number, if then change step S3-2, otherwise change step S3-6;
S3-2, since first, according to first outNode set, expansion obtains the set Node1 of first child node, again according to the outNode set of first child node, obtains the child node set Node2 of child node.Cost adds up in the expansion process, and first node of mark is to the bee-line of this node; And the like, expansion
Inferior, obtain gathering NodeR, NodeS be set be set Node1, Node2 ..., the union of NodeR;
S3-3, from described second, inNode set according to second, expansion obtains the set Node1 ' of second child node, again according to the inNode set of second child node, obtain that cost adds up in the child node set Node2 ' expansion process of child node, this node of mark is to the bee-line of Section Point; , and the like, expansion
Inferior, obtain gathering NodeR '; Set NodeS ' be set be set Node1 ', Node2 ' ..., the union of NodeR ';
S3-4 obtains the common factor of set NodeS and set NodeS ', and obtains a node m therein, adds up to m from first and goes up m to the second cost sum minimum, and m is first o'clock to the second o'clock intermediate node in the shortest path;
S3-5 utilizes the method for recurrence, obtains at first to the shortest path of m and m to the second shortest path;
S3-6, since first, outNode set according to first, expansion obtains the set Node1 of first child node, again according to the outNode set of first child node, obtain that cost adds up in the child node set Node2. expansion process of child node, first node of mark is to the bee-line of this node, and the like, expansion
Inferior, obtain gathering NodeO, set NodeP be set be set Node1, Node2 ..., the union of NodeO;
S3-7, from described second, inNode set according to second, expansion obtains second the set Node1 ' of child node, again according to the inNode set of second child node, obtains the child node set Node2 ' of child node, cost adds up in the expansion process, the bee-line of this node to the second of mark node, and the like, expansion
Inferior, obtain gathering NodeO '; NodeP ' be set be set Node1 ', Node2 ' ..., the union of NodeO ';
S3-8 gets a less set of set NodeP and the middle number of nodes of NodeP ' and expands once again, obtains gathering NodeQ;
S3-9, obtain set that does not have expansion among set NodeP and the NodeP ' and the common factor of gathering NodeQ, and in this common factor, obtain a node m, and adding up to m from first and go up m to the second cost sum minimum, m is first o'clock to the second o'clock intermediate node in the shortest path;
S3-10 utilizes the method for recurrence, obtains at first to the shortest path of m and m to the second shortest path.
7, the lookup method of shortest path between node among the figure as claimed in claim 1 is characterized in that, and is further comprising the steps of after step S2:
S3 preserves shortest path information, nodal information, coded message and maximum hop count k information between described first and second.
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| CN102262687A (en) * | 2010-05-29 | 2011-11-30 | 比亚迪股份有限公司 | Methods for searching path and calculating wire length in wire harness network |
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| CN104462260B (en) * | 2014-11-21 | 2018-07-10 | 深圳大学 | A kind of community search method in social networks based on k- cores |
| CN105550765B (en) * | 2015-11-30 | 2020-02-07 | 中国科学技术大学 | Method for selecting representative elements in road network distance calculation |
| CN105550765A (en) * | 2015-11-30 | 2016-05-04 | 中国科学技术大学 | Method for selecting representative elements in road network distance calculation |
| CN107679049A (en) * | 2016-08-02 | 2018-02-09 | 北京京东尚科信息技术有限公司 | Obtain the method, apparatus and system of the hop of tree structure data two |
| CN108573001A (en) * | 2017-03-14 | 2018-09-25 | 华为技术有限公司 | Method and apparatus for determining shortest path distance |
| CN108595603A (en) * | 2018-04-20 | 2018-09-28 | 北京费马科技有限公司 | Inquiry is without the method for point-to-point transmission shortest path and application in weight graph in chart database |
| CN108595603B (en) * | 2018-04-20 | 2021-07-02 | 深圳神图科技有限公司 | Method for inquiring shortest path between two points in weightless graph in graph database and application |
| CN111506613A (en) * | 2020-04-22 | 2020-08-07 | 支付宝(杭州)信息技术有限公司 | Method, system, device and equipment for querying incidence relation of data record |
| CN113421316A (en) * | 2021-06-30 | 2021-09-21 | 亿图软件(湖南)有限公司 | Connection line path construction method and device, computer equipment and readable storage medium |
| CN113421316B (en) * | 2021-06-30 | 2023-03-28 | 亿图软件(湖南)有限公司 | Connection line path construction method and device, computer equipment and readable storage medium |
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