A Transmission Scheduling Method for Wireless Sensor Networks Based on Edge Coloring

Abstract

The present invention discloses a transmission scheduling method for edge coloring, which comprises the following steps: Step 1, converting a wireless sensor network into a graph structure; Step 2, updating edges and selecting edges that meet the conditions as candidate edges and putting them into set S; Step 3, initializing queue Q, putting the edges in S into Q, then taking out an edge e from Q and reassigning colors; Step 4, allocating a time slot for communication between two sensors according to the color of the edge. The present invention provides a transmission scheduling for a dynamic wireless sensor network based on edge coloring. Compared with traditional methods, it does not require recalculation, has high accuracy and fast calculation speed.

Description

Technical Field

[0001] The present invention belongs to the field of wireless sensor network technology, and is a transmission scheduling method for wireless sensor networks based on edge coloring. Background Art

[0002] In recent years, the deployment and design of wireless sensor networks have received increasing attention. Wireless sensors have a wide range of applications in data collection and monitoring. These applications include environmental climate monitoring, traffic condition monitoring, and search and rescue, etc. A sensor network is a computer network composed of many sensors distributed in space.

[0003] The transmission scheduling of wireless sensor networks plays an important role in improving the timeliness and energy efficiency of data dissemination and data collection, which are important performance indicators of sensor networks. In the past, sensor networks usually adopted the CSMA / CA algorithm to avoid transmission conflicts. However, CSMA / CA can only try to avoid conflicts, and the effect is not very obvious. And if CSMA / CA is used, it may waste energy because the receiver is constantly listening to the channel. In contrast, TDMA can more easily determine when to listen to the channel and when to transmit, so it can completely avoid collisions, provide a bounded access delay, and achieve higher energy efficiency.

[0004] TDMA divides time into periodic frames, and each frame is further divided into several time slots (both frames and time slots do not overlap with each other). Each time slot is a communication channel and is assigned to a sensor. According to a certain time slot allocation principle, each sensor can only transmit signals to other sensors in the specified time slot within each frame. Under the conditions of meeting timing and synchronization, sensors can receive the signals of other sensors in each time slot without interference. At the same time, the signals sent by sensors to other sensors are all arranged in the predetermined time slots for transmission. As long as each sensor receives in the specified time slot, it can distinguish the signal sent to it from the combined signal (TDM signal). The TDMA system transmits data using the buffer-burst method, so the transmission for any one sensor is discontinuous.

[0005] The main challenge in adopting the TDMA protocol in a sensor network is to allocate time slots for each pair of adjacent nodes. This problem is called link scheduling. To avoid conflicts, a feasible time slot allocation should be such that one neighbor of the receiving node should transmit in the time slot; other neighbors may receive during the time slot. A simple method for feasible time slot allocation is to assign a unique time slot to each pair of neighbors in the network. Although this eliminates the possibility of conflicts, the large number of time periods required increases the communication delay. Therefore, a feasible transmission scheduling scheme is needed that uses the minimum number of time periods.

[0006] Transmission scheduling involves allocating time slots to nodes or links. Of course, allocating a unique time slot to each node can avoid collisions, but it consumes too many time slots; allocating a unique time slot to each link can also avoid collisions, but it has the same drawback of consuming too many time slots. To effectively utilize time slots, node coloring for node scheduling or edge coloring for link scheduling can be adopted. The schedule is calculated through graph coloring to reduce the number of time slots used.

[0007] The link time slot allocation problem is closely related to the edge coloring problem of a graph. In an effective edge coloring, two edges on the same node are not assigned the same color. Vizing's theorem states that an effective edge coloring of a graph can be obtained using at most (δ + 1) colors, where δ is the maximum degree of a node in the graph. Given an effective edge coloring of the graph of a sensor network, the time slot allocation of sensor nodes can be obtained by mapping each time slot to a color.

[0008] Existing solutions for edge coloring mainly focus on static graphs. However, many graphs in the real world are highly dynamic. At the same time, sensor networks also change dynamically. For example, if a certain sensor is damaged, then the communication with that sensor is invalid. Recalculation is rather time-consuming. Therefore, the research on dynamic graphs is very valuable. Summary of the Invention

[0009] The object of the present invention is to design an effective dynamic edge coloring algorithm to schedule the transmission of a sensor network and effectively solve the transmission conflict problem.

[0010] The technical solution for achieving the object of the present invention is as follows: A transmission scheduling method for a dynamic wireless sensor network based on edge coloring, comprising the following steps:

[0011] Step 1: Convert a wireless sensor network with allocated time slots into an undirected unweighted graph G(V, E), where sensors are used as graph nodes V, the relationship between sensors is used as the edges E of the graph, and the allocated time slots between sensors are converted into corresponding colors;

[0012] Step 2: Insert or delete an edge e in G, put e into the set S, and select the edges that meet the conditions from the neighbor edges of e and put them into S;

[0013] Step 3: Initialize a queue Q, put the edges in S into Q, take out an edge from Q and reallocate colors according to the dynamic algorithm, and put the edges that need to be recolored into Q, and repeat running the dynamic algorithm until Q is empty;

[0014] Step 4: Allocate a time slot for the communication between two sensors according to the color of the edge.

[0015] Preferably, step 2 specifically includes the following steps:

[0016] Step 201, insert or delete an edge e and update the stored structure. The newly inserted edge is not assigned a color first.

[0017] Step 202, put e into the set S, traverse the neighbor edges of e, and put the edges with a priority higher than e and a color smaller than e into S.

[0018] Preferably, the method for judging the priority is as follows: Given two edges (u, v) and (u′, v′), assuming that the degree of u is greater than v and the degree of u′ is greater than v′, if one of the following conditions is satisfied:

[0019] · deg(u) > deg(u′)

[0020] · deg(u) = deg(u′), deg(v) > deg(v′)

[0021] Then (u, v) has a higher priority than (u′, v′), where deg represents the degree of a node;

[0022] When deg(u) = deg(u′) and deg(v) = deg(v′), the edge with a smaller id has a higher priority.

[0023] Step 3 specifically includes the following steps:

[0024] Step 301, initialize a queue Q, put the edges in S into Q, and take out an edge e from Q;

[0025] Step 302, collect the colors of the edges with a higher priority than e and put these colors into the set C;

[0026] Step 303, recalculate the color of edge e. The specific calculation formula is:

[0027]

[0028] where e.color represents the color of e, N represents natural numbers, and C represents the set of colors collected in step 302.

[0029] Step 304, if the color re - assigned to e is different from the original color of e, put the edges with a lower priority than e into the queue Q, and repeat steps 302, 303, and 304 until the queue is an empty set.

[0030] Compared with the prior art, the significant advantages of the present invention are as follows: On the one hand, it can ensure that the number of colors used for coloring is small, that is, the number of time slots used is small. On the other hand, it avoids some unnecessary calculations and optimizes the calculation time.

[0031] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable, the following will be described in detail in conjunction with the preferred embodiments and with reference to the accompanying drawings. Description of the Drawings

[0032] Figure 1 It is an example diagram of edge coloring.

[0033] Figure 2 It is an example diagram of Algorithm 1 after updating the figure.

[0034] Figure 3 It is a flowchart of the dynamic coloring algorithm. Detailed Embodiment

[0035] A wireless sensor network transmission scheduling method based on edge coloring, the specific steps are as follows:

[0036] Step 1, convert a wireless sensor network into an undirected and unweighted graph G(V, E), where V(G) represents the set of nodes and E(G) represents the set of edges in G. Denote the number of nodes as n and the number of edges as m. Each node has a unique id, denoted by id(u, G) for the id of node u. Use nbr(u, G) to represent the neighbors of u. Use deg(u, G) to represent the degree of node u, that is, the number of neighbors of u. At the same time, the edges in G are given a definition of priority according to the degree:

[0037] Definition 1.1 (Priority of edges) Given a graph G and two edges h = (u, v) and e′ = (u′, v′) ∈ E(G) (assuming the degree of u is greater than v and the degree of u′ is greater than v′). If one of the following conditions is satisfied:

[0038] · deg(u) > deg(u′)

[0039] · deg(u) = deg(u′), deg(v) > deg(v′)

[0040] Then e is prior to e′ (denoted as e < e′);

[0041] For the case where deg(u) = deg(u′) and deg(v) = deg(v′), select the edge with a smaller id to be prior. Based on this comparison of priorities, all edges are sorted in order. In addition, use adj(h, G) to represent the set of adjacent edges of edge h in G. Use adj+(h, G) to represent the set of edges higher than edge e, and use adj-(h, G) to represent the set of edges with a lower priority than h.

[0042] Step 2, insert or delete an edge e in G, put e into the set S, and select the edges that meet the conditions from the neighbor edges of e and put them into S, that is, find the edge that is most likely to violate the minimum edge color property from the neighbor edges of e.

[0043] Definition 2.1 (Minimum Edge Color Property) Given a graph G and an edge coloring C, the color of edge e satisfies the minimum edge color property if

[0044] where e.color represents the color of e, N represents the set of natural numbers, and adj+(e, G) represents the edges with higher priority than e.

[0045] For simplicity, if all edge colors in C satisfy the minimum edge color property and are denoted as Ψ(G), then the edge coloring C is called a minimum edge coloring. The dynamic edge coloring problem is equivalent to maintaining Ψ(G) when the graph is updated. Obviously, there is the following lemma:

[0046] Lemma 1. Given a graph G and Ψ(G), when an edge e is inserted / deleted, for edge e′, if in graphs G and G±e, e′ < e, then e′.color(Ψ(G)) = e′.color(Ψ(G±e)).

[0047] According to Lemma 1, in Ψ(G) and Ψ(G±e), the colors of the edges that e always has a higher priority among before and after the update remain unchanged. Therefore, these edges do not need to be considered. Besides these edges, the colors of other edges may violate the minimum edge color property, so they need to be recolored. To make the colors of these remaining edges satisfy the minimum edge color property, their colors are reallocated according to the following formula 1:

[0048]

[0049] where C old and C new represent the edge colorings before and after the color reallocation of edge e, N represents the set of natural numbers, and adj+(e, G) represents the edges with higher priority than e. There is the following lemma:

[0050] Lemma 2. Given a graph G and Ψ(G), when an edge e is inserted / deleted, if the reallocation process starts with Ψ(G), when formula 1 is satisfied for all edges e ∈ G, the color C new is Ψ(G±e).

[0051] According to Lemma 2, the edge color property in Ψ(G) can be obtained by recursively reassigning the colors of the edges, and the minimum edge color property in Ψ can be obtained. The remaining problem is how to effectively perform the recursive recoloring process. A simple implementation is to scan the edges that may violate the minimum edge color property, reassign their colors round by round according to Formula 1, and terminate when no edge changes its color in that round. The disadvantage of this method is that in each round, all edges must be scanned and recolored, even if only one edge changes its color in that round. Additionally, according to Formula 1, only when the color of any edge in adj+(e′,G±e) changes its color does the edge e′ need to reassign its color. At the same time, the color change of e′ may further affect the colors of the edges in adj-(e′,G±e). Therefore, instead of traversing all the edges, start from the edges whose colors may violate the minimum edge color property due to the insertion / deletion of e, and reassign the colors of these edges. If the color of e′ changes, use the edges in adj+(e′,G±e) as candidate edges whose colors may violate the minimum edge color property, and continue the above process until no edge changes its color. According to this edge color propagation mechanism, there are the following lemmas:

[0052] Lemma 3. Given a graph G and Ψ(G), when inserting an edge e=(u,v), the different colors of e″.color(Ψ(G+e)) and e″.color(Ψ(G)) will cause the colors of other edges to change, where e″∈{(u,v),(u,u′),(v,v′)}∪{adj+(u,u′),G)∩adj+((u,u′),G+e),u′}∪{adj+((v,v′),G)∩adj+((v,v′),G+e)}, u′∈nbr(u,G), v′∈nbr(v,G).

[0053] Lemma 4. Given a graph G and Ψ(G), when deleting an edge e=(u,v), the different colors of e″.color(Ψ(G-e)) and e″.color(Ψ(G)) will cause the colors of other edges to change, where e″∈{(u,v),(u,u′),(v,v′)}∪{adj+(u,u′),G)∩adj+((u,u′),G-e),u′}∪{adj+((v,v′),G)∩adj+((v,v′),G-e)}, u′∈nbr(u,G), v′∈nbr(v,G).

[0054] According to Lemma 3 and Lemma 4, the dynamic edge coloring can be performed as follows: Select the edge e″ as a candidate edge and put it into S, and continuously propagate the edge color change until no new edge changes its color.

[0055] Step 3, initialize an empty queue Q and put the edges in S into Q. Specifically, it first pops an edge (u′, v′) from Q. Then, it calculates a new color C by traversing the edges with higher priority than (u′, v′). new . If C new is different from the existing colors, it assigns C new to (u′, v′) and pushes the edges with lower priority than (u′, v′) for further recoloring. When Q becomes an empty set, the algorithm is completed. Figure 1 Show an instance of a graph with colors assigned, Figure 2 show the result after inserting an edge (v6, v9). At this time, all the edges that need to be recolored have completed the color reassignment, and after the reassignment, it can be ensured that any two adjacent edges have different colors and use the fewest colors.

[0056] Step 4: Allocate a time slot for the communication between two sensors according to the color of the edge. Each color has a unique corresponding time slot, and through the dynamic coloring algorithm, it can be ensured that a sensor does not communicate with multiple other sensors at the same time.

[0057] Algorithm 1: Heuristic-based dynamic edge coloring algorithm

[0058]

Claims

1. A transmission scheduling method for a dynamic wireless sensor network based on edge coloring, characterized in that Including the following steps: Step 1: Convert a wireless sensor network with allocated time slots into an undirected and unweighted graph G(V, E), where sensors are graph nodes V, the relationship between sensors is the edge E of the graph, and the allocated time slots between sensors are converted into corresponding colors; Step 2: Insert or delete an edge e in G, put e into set S, and select edges that meet the conditions from the neighbor edges of e and put them into S; Step 3: Initialize a queue Q, put the edges in S into Q, take out an edge from Q and re-allocate colors according to the dynamic algorithm, and put the edges that need to be recolored into Q, and repeat running the dynamic algorithm until Q is empty. Specifically, it includes the following steps: Step 301, Initialize a queue Q, put the edges in S into Q, and take out an edge e from Q; Step 302, Collect the colors of the edges with higher priority than e, and put these colors into set C; Step 303, Recalculate the color of edge e. The specific calculation formula is: where e.color represents the color of e, N represents natural numbers, and C represents the set of colors collected in step 302; Step 304, If the color re-allocated to e is different from the original color of e, put the edges with lower priority than e into queue Q, and repeat steps 302, 303 and 304 until the queue is an empty set; Step 4: Allocate a time slot for the communication between two sensors according to the color of the edge.

2. The transmission scheduling method for a dynamic wireless sensor network based on edge coloring according to claim 1, wherein, Step 2 specifically includes the following steps: Step 201, Insert or delete an edge e, and update the stored structure. The newly inserted edge is not allocated a color first; Step 202, Put e into set S, traverse the neighbor edges of e, and put the edges with higher priority than e and whose colors are less than e into S.

3. The transmission scheduling method for a dynamic wireless sensor network based on edge coloring according to claim 2, wherein The method for judging the priority is as follows: Given two edges (u, v) and (u ′ , v ′ ), assuming that the degree of u is greater than that of v and the degree of u' is greater than that of v', if one of the following conditions is satisfied: ●deg(u)>deg(u′) ●deg(u)=deg(u′), deg(v)>deg(v′) Then (u, v) is prior to (u′, v′), where deg represents the degree of the node; When deg(u)=deg(u′) and deg(v)=deg(v′), the edge with a smaller id is prior.

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