CN116208967A - Efficient and reliable virtual backbone network construction method - Google Patents
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Abstract
Virtual backbones are commonly employed in large-scale wireless sensors to achieve efficient transmission of information. How to construct a virtual backbone with efficient transmission and a certain fault tolerance is one of the important research hotspots in the current academia. The problem of constructing a virtual backbone network can be converted into a constructed communication control set problem in graph theory to solve, the problem of solving the minimum communication control set has been proved to be an NP complete problem, and the communication support set scale obtained in the time of an approximate algorithm polynomial can be limited to a specific constraint range through strict theoretical analysis and verification. The invention provides a virtual backbone network construction algorithm which simultaneously considers efficient routing and fault tolerance, the algorithm adopts m-weight control to improve the fault tolerance of the routing, and the time complexity is O (n) 3 ) And the virtual backbone route and the original route are controlled under the constraint condition of 5 times route. When m is less than or equal to 5, the approximate ratio of the communication control set is 54opt (1，m) The method comprises the steps of carrying out a first treatment on the surface of the When m is>5, the connectivity control set approximatesThe ratio is 53opt (1，m) Wherein opt (1，m) Refers to the optimal solution of m-way control set problem. The effectiveness of the approximation algorithm herein was verified by comparative experiments.
Description
Technical Field
The invention belongs to the field of network communication, and particularly provides a method for constructing a route constraint virtual backbone network by considering fault tolerance in a wireless sensor network.
Background
The wireless sensor network (wireless sensor network, WSN) is widely applied to various application scenes such as environment monitoring, health application, disaster relief, battlefield monitoring, traffic control, mobile computing, military operations and the like due to the characteristics of low cost, easy deployment, convenient use and the like. In the deployment process of large-scale wireless sensors, particularly in a field environment monitoring scene, the wireless sensors are often thrown in a coverage area in a large quantity and randomly and uniformly, so that the constructed wireless sensor network is extremely easy to cause the problems of congestion, excessive consumption of backbone nodes, unstable network topology, short network life cycle and the like in the information collection and transmission process. In order to solve the above problems, policies such as hierarchical clustering routing and virtual backbone routing are often adopted to guide information to be directionally transmitted in some specific wireless sensor networks, and because of the reasons of movement and failure of nodes, the topology structure of the network is unstable, so that a virtual backbone network with fault tolerance needs to be constructed. In graph theory, this problem can be solved by constructing a connected control set by using a k-connected m-control set algorithm, namely, any point except the virtual backbone network C is required to be controlled by at least m points in the C, and the connectivity of the sub-graph derived by the C is at least k. The (k, m) -CDS is used as a virtual backbone, and even if each node of min { k-1, m-1} fails, the virtual backbone still can work normally. And (5) conveying. The virtual backbone technology was proposed by Ephremides [1] in 1987 and is widely supported and adopted by academia. In a virtual backbone network, each node sends messages to backbone nodes in an adjacent virtual backbone network, and the messages are forwarded to its destination node along a virtual routing network of those backbone nodes. Therefore, when the route path searching space is limited in the virtual backbone network, shorter route path searching time, smaller route table and more convenient route maintenance can be obtained, thereby greatly improving the forwarding efficiency of the wireless sensor network and prolonging the life cycle of the network.
In a virtual backbone network, the length of transmission paths between nodes in the network is typically measured in terms of average backbone path length (the Average Backbone Path Length, ABPL), indirectly reflecting the cost or energy consumption of information transmission in the network. The virtual backbone network construction problem in the wireless sensor network is converted into a communication control set (connected dominating set, CDS) 3 problem in graph theory, and Du, ding, zhang and other scholars develop researches on the virtual backbone network with characteristics of routing constraint, minimum weight, error tolerance and the like, a series of derivable and verifiable approximation algorithms are designed, and a theoretical method is provided for constructing an extremely small virtual backbone network under specific constraint through the communication control set. In 2010 Ding [4] has proposed the problem of minimum routing cost CDS (MOC-CDS), a shortest path pi (u, v) must exist between any two nodes u, v in MOC-CDS, and all nodes in pi (u, v) \ { u, v } belong to MOC-CDS. In 2011, in order to reduce the scale of the virtual backbone network and ensure a certain network transmission efficiency, ding [5] raised the problem of alpha-time routing constraint (alpha MOC-CDS), which requires that the shortest path length of any two nodes through the virtual backbone network is not more than alpha times the shortest path length of two nodes in the original network. As shown in fig. 1, the gray backbone nodes form a connected virtual backbone network, and the white nodes are ordinary nodes in the network. In the left diagram of fig. 1, the virtual backbone network nodes are {8, 7, 6, 5, 4, 3}, and the transmission paths of the node 1 and the node 2 are 1-8-7-6-5-4-3-2; in the right diagram of fig. 1, after one backbone node 1 is added, the virtual backbone nodes are {8, 7, 6, 5, 4, 3, 1}, and the transmission paths of the nodes 1 and 2 are 1-2.
In some specific wireless sensor networks, the topology of the network is unstable due to movement, failure, etc. of the nodes, so that a virtual backbone network with fault tolerance needs to be constructed. In graph theory, this problem can be solved by constructing a connected control set by using a k-connected m-control set algorithm, namely, any point except the virtual backbone network C is required to be controlled by at least m points in the C, and the connectivity of the sub-graph derived by the C is at least k. The (k, m) -CDS is used as a virtual backbone, and even if each node of min { k-1, m-1} fails, the virtual backbone still can work normally.
Disclosure of Invention
[ object of the invention ]: the invention provides a route constraint virtual backbone network construction method considering fault tolerance, which can ensure that any m-1 backbone nodes in a network are invalid, a non-backbone node still can control the backbone nodes, and meanwhile, compared with a traditional virtual backbone network, the method effectively reduces the transmission hop count among all nodes in the network and reduces delay.
[ technical scheme ]: the technical scheme of the invention is as follows:
1. building virtual backbone networks
The problem of building a virtual backbone can be translated into the problem of building a connectivity control set (CDS) in graph theory. In a wireless sensor network, the network topology is described by a graph g= (V, E), V representing all nodes in the network and E representing all edges in the network. C is a subset of V, and if each vertex in V\C has neighbors in C, then subset C is referred to as the control set. If the subgraph G [ C ] derived from C is connected, then C is referred to as a connected control set. For easy understanding, the basic concepts are explained as follows
Define 2 control Set (DS). For a given subset S of unit disk graph g= (V, E), which is called a control Set of G, then for any node u E V, either u E S, or u has at least one neighbor in S.
Defining 3 a set of connectivity controls (connected dominating set, CDS) given a unit circular graph g= (V, E), a subset S is called a set of connectivity controls for G, S must satisfy the following two conditions (1) S is a set of controls for G; (2) Subgraph G [ S ] derived from S]Is bidirectionally connected, i.e. G [ S ]]A two-way path exists between any two points, so that two points can be separatedTo transmit information to each other. Definition 1: k-connected m-control set: given that one of the sets of connected control D in a graph g= (V, E) is a subset of k-connected m-controls if and only if any size does not exceed k-1
So that G [ D-D ]']Still connected, there is one m control set where the connected control set D is G if and only if any section for the trunk occupies u ε V-D. u has at least m neighbors in D.
2. Considering routing constraints
Information transfer is via the virtual backbone, if one non-CDS node wants to send a message to another non-CDS node, it first sends the message to the neighboring CDS node. The search range of the route is then narrowed down into the CDS. After a message is accepted by a neighboring CDS node that is relayed to the destination, the node may pass the message to the destination. This can cause significant delays in time, and we use an alpha-routing constrained virtual backbone network (alpha MOC-CDS) to solve the above problem, considering the aging problem of information exchange.
Definition 4: minimum routing cost virtual backbone (MOC-CDS):
MOC-CDS is to find a minimum set of points
This set D has the following characteristics:
1)
let (u, v) E E. />
2) The derived subgraph G [ D ] is connected.
3)
If Dist (u, v)>1, then->
Wherein p is i (u,v)＝{u,w 1 ,w 2 ,…,w k V, representing the i-th shortest path between points u, v; dist (u, v) represents the shortest path hop number between points u, v; p (P) i (u, v) represents all shortest paths between u, v.
Definition 5: alpha routing constraint connectivity control set (alpha MOC-CDS):
alpha MOC-CDS represents a set of points
This set D has the following characteristics:
1)
let (u, v) E E.
2) The derived subgraph G [ D ] is connected.
3)
If Dist (u, v)>1, then p D All intermediate nodes on (u, v) belong to D and D D (u,v)≤α*d(u,v)。
Wherein p is D (u, v) represents the shortest path between u, v on D; p (u, v) represents the shortest path between u, v; d, d D (u, v) and d (u, v) each represent p D Number of intermediate nodes on (u, v) and P (u, v).
Definition 7: k-connected m-control set: given that one of the sets of connected control D in a graph g= (V, E) is a subset of k-connected m-controls if and only if any size does not exceed k-1
So that G [ D-D ]']Still connected, there is one m control set where the connected control set D is G if and only if any section for the trunk occupies u ε V-D. u has at least m neighbors in D.
Definition 8: the problem of α -fold routing constraint considering fault tolerance (1, m) - αmoc-CDS:
given a unit torus g= (V, E), the subset S is called a connectivity control set of G that takes into account fault tolerance α -routing constraints, S must satisfy the following four conditions:
(1) S is a control set of G;
(2) The sub-graph Gs derived by S is connected, namely, at least one path exists between any two points in the Gs, so that information can be mutually transmitted between the two points;
3. proof of theory
The problem of finding the minimum route cost connectivity control set has proven to be an NP-hard problem, and some documents propose to solve this problem by finding an approximation algorithm for MOC-CDS. These approximation algorithms generally fall into two phases: constructing a very large independent set in the first stage; in the second stage, some other nodes are added as connecting nodes to communicate with the extremely large independent set to form a complete minimum routing cost communication control set. The lemma 1 will provide theoretical support for the second stage of the algorithm.
The quotation 1:G shows a connected graph, and D shows a connected control set of G. d (u, v) represents the shortest length of two points u, v in the graph G, d D (u, v) represents the shortest path length of the intermediate node connecting the u, v two points all in D. Let d be present for any pair of nodes u, v satisfying d (u, v) =2 D (u, v) -1. Ltoreq.alpha, then d D (u,v)-1≤α(d(u,v)-1)。
The lemma 2G represents a graph of connectivity, and D represents a connectivity control set of G. It is assumed that any pair of nodes u, v,
all have d D (u,v)-1≤α,
Then d D (u,v)≤αd(u,v)
The lemma 3:I represents a very large independent set of graph G. D represents a connectivity control set containing I. It is assumed that the set of nodes u, v, which arbitrarily satisfy d (u, v). Ltoreq.4 and where u, v are both in I,
all have d D (u,v)≤4，
Then d D (u,v)≤5d(u,v)
Du demonstrates axicon 1, axicon 2 and axicon 3. From these three arguments we can learn that in the undirected graph G, after finding the control set C for G, all nodes in C are put into D. If any pair of nodes u, v E D and D (u, v)<4 adding all nodes of the shortest path between u and v to D, we can get D D (u, v) is less than or equal to 5d (u, v). Attakorn offers improvements in routing constraints in heterogeneous networks. Inspired by this improvement, we can consider undirected graphs G and GControl set C. If any pair of nodes u, v E D and D (u, v)<3 we add all nodes of the shortest path between u and v to D, we can get D as well D (u, v) 5d (u, v), theoretical analysis process such as primer 4.
The quotation 4:I represents a very large independent set constructed in one stage, D represents one connectivity control set containing I, if for each pair of nodes u, v belonging to I, if they satisfy D D (u, v). Ltoreq.3, then find a shortest path between them and put all points on that path into S, then they induce sub-graph G [ S ]]Is connected and satisfies d for any pair of nodes u, v in the graph D (u,v)≤5d(u,v)。
And (3) proving: consider a pair of nodes u, V in V whose shortest path in graph G is k, assuming that this path is (u=w 0 ,w 1 ,w 2 …w k-1 ,v＝w k ) (as shown in FIG. 2), known as GS]Is connected to each adjacent pair w in the path i And w i+1 (1) if w i And w i+1 One is the node in I, we assume w without loss of generality i Not nodes in I. Then dom in the reproduction graph G D (w i ) And w i There must be a path through only the points in D and less than or equal to 3. (dot) D (w i ) The dominant w in the representation I i Is a node of (2)
(2) If w i And w i+1 None are nodes in I. Then there is dom D (w i ) And dom (dot) D (w i+1 ) Respectively govern w 1 And w 2 . No matter how D (w i ) And dom (dot) D (w i+1 ) Whether or not they are the same point, there is dot in the graph G D (w i ) And dom (dot) D (w i+1 ) There must be a path through only the points in D and less than or equal to 3. And because a path of length 3 (dom) exists in the original image G which is obtained by the known condition D (w i ),w i ,w i+1 ,dom D (w i+1 ))。
Then we can derive:
d D (u,v)≤d(u,dom D (u))+d(dom D (v),v)
+∑ 0≤i≤k d D (dom D (w i ),dom D (w i+1 ))≤3k+2≤5k＝5d(u,v)
wherein k is greater than or equal to 1, dom C (u) represents the point in set C where u is controlled.
4. Algorithm design
The approximation algorithm of the virtual backbone network is generally divided into two stages, wherein the first stage constructs a maximum independent set which is also a control set; in the second stage, by adding other points as connection points, the points in the control set are connected to form a connected control set. According to lemma 4, we can construct the αmoc-CDS first. The first stage is to construct a maximum independent set considering the weight as a control set, we use algorithm 1 as a stage to construct MIS, and the algorithm greedy node with minimum searching node degree is used as a backbone node, and finally a maximum independent set is formed. And in the second stage, for any pair of nodes u, v which satisfy d (u, v) less than or equal to 3 in DS, the shortest path between the u and v points in the graph G is obtained, and the points in the path are added into the set C.
The quotation 5, undirected graph G= (V, E) is a unit disk graph, m is a natural number and δ (G). Gtoreq.m-1. Make the following steps
Represents the minimum (1, m) -CDS of one graph G, S represents one MIS of the graph G. Then we can get
For the designed approximation algorithm of the minimum 1-connected m-control set problem, we will start in this section with the simplest case of m=1. The basic idea of the algorithm is: the αmoc-CDS is first generated using the methods set forth in algorithm 1 and algorithm 2, and then one (m-1) MIS is generated using algorithm 1 in turn, such that each non-backbone node is controlled by vertices in more than m backbone nodes. The algorithm is as follows.
Next, we give the upper bound of (1, m) -alpha MOC-CDS (theorem 1)
In this section we will give an approximate ratio of the (1, m) - αmoc-CDS algorithm in this chapter and prove.
If I is a very large independent set, then for any u ε I, |{ v ε I|0<d (u, v) < 3} | < 48)
The connected set of lemmas 7, consisting of the second stage, has the following property |C' | 48| I|, where I is the very large independent set built in the first stage.
And (3) proving: a graph G is constructed, wherein the node set I and the edge set { (u, v) |u, v, ∈I,0<d (u, v) +.ltoreq.3 } are found, and the maximum degree of the nodes in G is 48 according to the quotients 5. So G contains up to 24I edges, in the second stage, because d (u, v) is 3, up to two points are added between each pair of maximum independent set nodes,
so |c' | is less than or equal to 2.24|i|=48|i|.
Lemma 8_: in the (1, m) -alpha MOC-CDS constructed by algorithm 3, when m.ltoreq.5,
when m is>5 times, the->
Wherein->
Minimum (1, m) -CDS representing a graph G
And (3) proving: order the
From algorithm 3, it can be known that I i \S i Is an independent set and +.>
Therefore, from the theory 5, we know +.>
Can then be pushed out
And because of
It can be derived that when m.ltoreq.5, & gt>
When m is>5 times, the->
Lemma 9_: the upper bound size of the connectivity control set D constructed in the (1, m) - αmoc-CDS constructed in algorithm 3 is as follows: when m is less than or equal to 5, the value is 53opt (1，m) ，m>At 5, 54opt (1，m) At the same time, for any pair of nodes u, v, d is present D (u,v)≤5d(u,v)。
And (3) proving: from the quotation 7 and the quotation 8, it can be seen that:
when k is>And when 5, the content of D is less than or equal to C' ++ I 1 ∪…∪I m |≤48·|I 1 |+|I 1 ∪…∪I m |≤53opt (1，m) ，
When k is less than or equal to 5, |D| is less than or equal to |C' |+|I 1 ∪…∪I m |≤48·|I 1 |+|I 1 ∪…∪I m |≤54opt (1，m)
From the lemma 4, it is known that in D, any pair of nodes u, v has D D (u, v) is less than or equal to 5d (u, v). While each non-backbone node is dominated by more than m backbone nodes. Wherein opt (1，m) Refers to the optimal solution of the very small (1, m) -CDS.
[ beneficial effects ]: the invention has the significance of providing a weight-considered route constraint virtual backbone network construction method, which can effectively save energy, prolong the service life of a network, ensure abundant energy of nodes, effectively reduce the number of transmission hops between each node in a heterogeneous sensor network and reduce delay by constraining the path length. The S finally derived by the algorithm αMOC-WCDS is bounded by 163.5179opt+180.0309.
[ description of the drawings ]:
two CDS with gray nodes of FIG. 1 as backbone nodes
Fig. 2 connects the shortest paths of u, v (u=w0, w1, w2 … wk-1, v=wk);
3 algorithm CDS sizes at a transmission distance of 15 in FIG. 3;
figure 4 CDS size for 3 algorithms at a transmission distance of 20;
figure 5 CDS size for 3 algorithms at a transmission distance of 25;
fig. 6 size of backbone network for transmission radius 20;
fig. 7 average backbone path length for a backbone network with a transmission radius of 20;
fig. 8 shows the total weight of backbone nodes of the backbone network in case of a transmission radius of 20;
specific embodiment(s):
experimental environment
The computer platform performance based on the experiment is as follows:
RAM 16.0GB
System type 64 bit operating system, x64 based processor
Programming IDE: matlab programs IDE: matlab
Parameters of a wireless sensor network
In the simulation, parameters of the wireless sensor network having different transmission ranges are set as follows. First, the sensor is modeled by a set of nodes randomly deployed on a euclidean plane bounded by 100 x 100. The total number of the nodes is 100, 200, 300 and 400 respectively; transmission radii are 15, 20 and 25, respectively; constructing 100 random graphs for each set of parameters; 100 experiments were performed for each random pattern to average.
Experimental results and analysis
Finally, comparing simulation results by using CDS sizes of different transmission radiuses in the experiment, wherein the description and analysis of the simulation results under the condition that the transmission radius is 15 are shown in figure 3; a description of the simulation result in the case where the transmission radius is 20 is shown in fig. 4; a description of the simulation result in the case where the transmission radius is 25 is shown in fig. 5.
Currently only solutions to the (k, m) -connectivity control set problem and the α -routing constraint connectivity control set (αmoc-CDS) problem, respectively, consider fault tolerance, and not to the simultaneous fault tolerance and α -times routing constraint problem solutions. The GOC-MCDS-D algorithm proposed by Du et al [10] is one of the best algorithms known at present for solving the alpha-times routing constraint CDS, and the shortest path selection strategy in the second stage is improved in consideration of fairness of algorithm comparison so as to be consistent with the shortest path selection strategy in the second stage, but the algorithm efficiency is not affected. The modified GOC-MCDS-D algorithm was designated in the experiment as MOC-CDS and compared to the algorithms herein (1, 2) -MOC-CDS and (1, 3) -MOC-CDS.
Figures 3, 4 and 5 show simulation results of the sizes of the MOC-CDS, (1, 2) -MOC-CDS and (1, 3) -MOC-CDS algorithms, and it can be seen in the three figures that the average size of CDS generated by each algorithm increases slightly as the total number of sensor nodes increases from 100 to 400. This is reasonable because all algorithms require more intermediate nodes on the shortest path to connect more control nodes to build the CDS. Meanwhile, as the total number of sensor nodes increases from 100 to 400, the three algorithm backbone node growth rates are decreasing. This is reasonable because with the canvas total size unchanged, the entire sensor network becomes quite dense as the number of nodes increases, fewer nodes are needed to perform algorithm 1 and algorithm 2, and the backbone network nodes gradually become saturated as the network becomes dense. Furthermore, we can see the algorithm MOC-CThe average size of CDS generated by DS is limited by our approach 8 approximation ratio. Meanwhile, by comparison experiments, the CDS size required to be increased by 15% and 30% for constructing the (1, 2) -MOC-CDS and the (1, 3) -MOC-CDS at the transmission radius of 15, 20 and 25 is an acceptable range, and the feasibility of the (1, m) -MOC-CDS algorithm is verified. In summary, the (1, m) -MOC-CDS algorithm effectively solves the problem of alpha-times route constraint considering fault tolerance, and fully considers the problem of fault tolerance of the whole network under the condition that the alpha-times route constraint (alpha is more than or equal to 5) is satisfied. The validity of the (1, m) -alpha MOC-CDS can be verified through experiments, and the former quotation 9 proves that d can be obtained for any pair of nodes u, v D (u,v)≤5d(u,v)。
The invention researches a virtual backbone network construction algorithm with fault tolerance in the wireless sensor network, and the algorithm simultaneously considers two constraints of fault tolerance and routing constraint. The virtual backbone network constructed based on the algorithm can effectively reduce the transmission hop count among nodes in the wireless sensor network, reduce the transmission delay, and the network has certain robustness and fault tolerance and longer life cycle. Theoretical analysis and simulation experiments prove that the method has smaller approximation ratio and smaller running time.
Claims (3)
1. The virtual backbone network construction approximation algorithm which gives consideration to high-efficiency transmission and fault tolerance is provided for the first time, and an approximate optimal solution can be obtained in polynomial time; the theoretical analysis derives the approximate ratio of the algorithm on each fault-tolerant space (m weight control set, m is less than or equal to 5 and m is more than 5), and the effectiveness of the algorithm is verified by comparison experiments.
2. The upper bound size of the communication control set algorithm D constructed by the (1, m) -alpha MOC-CDS is as follows:
when m is less than or equal to 5, the value is 53opt (1，m) ，
When m > 5, it is 54opt (1，m) ，
At the same time, for any pair of nodes u, v, d is present D (u，v)≤5d(u，v)。
3. The centralized algorithm composed of two stages solves the problem of alpha times routing constraint considering fault tolerance. Construction of (1, m) -alpha MOC-CDS Algorithm 1, algorithm 2 and Algorithm 3
The specific proof procedure is given in [18 ]. For the designed approximation algorithm of the minimum 1-connected m-control set problem, we will start in this section with the simplest case of m=1. The basic idea of the algorithm is: the αmoc-CDS is first generated using the methods set forth in algorithm 1 and algorithm 2, and then one (m-1) MIS is generated using algorithm 1 in turn, such that each non-backbone node is controlled by vertices in more than m backbone nodes. The algorithm is as follows.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117389941A (en) * | 2023-10-26 | 2024-01-12 | 苏州工业园区服务外包职业学院(苏州市服务外包人才培养实训中心) | Fault tolerance upper bound solving method and device for interconnection network structure |
| CN117389941B (en) * | 2023-10-26 | 2024-03-22 | 苏州工业园区服务外包职业学院(苏州市服务外包人才培养实训中心) | Fault tolerance upper bound solving method and device for interconnection network structure |
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