Boundary Recognition in Sensor Networks. Ng Ying Tat and Ooi Wei Tsang

Transcription

1 Boundary Recognition in Sensor Networks Ng Ying Tat and Ooi Wei Tsang School of Computing, National University of Singapore ABSTRACT Boundary recognition for wireless sensor networks has many applications, such as routing and ensuring that network coverage is sufficient. For a large number of sensor nodes that would have been deployed, equipped with only connectivity information, they are able to discern which nodes are at the boundary. There have been a number of algorithms proposed to solve this problem but due to the limitation of sensor nodes, in terms of computational power and lifespan, some of these algorithms might not be adequate. In this project, an algorithm that promises good performance with a minimal set of assumptions is explored and modifications were incorporated. Since it is a distributed algorithm, points in the algorithm where the nodes need to be synchronized were identified. With the implementation of the algorithm, the nodes that are close to the boundaries would be able to be identified. 1 INTRODUCTION Boundary recognition is closely linked with the issue of network coverage. Sensor networks are deployed to surveil an area of interest and it is important that it has adequate coverage. A boundary that is detected within an area of interest, a hole, would mean that there is inadequate coverage and deployment of additional sensor nodes would be necessary. Boundary recognition also helps in routing in wireless sensor networks. Funke tells us of a few protocols which uses network topology to facilitate routing (2005). Li & Liu proposes the Rendered Path (REP) protocol which uses boundary recognition as a stepping stone to estimate node-to-node distances and calculate node locations (2007). We can classify methods for boundary recognition into two categories, statistical and geometrical/topological. Statistical methods are based on the observation that certain phenomenon occurs more frequently to nodes at the boundary than other nodes. Geometrical/ topological methods use the geometrical/topological properties of the network connectivity graphs in finding holes and boundaries in the network. When we are searching for an answer to the boundary recognition problem; we should try to minimize the set of assumptions such that they are as general and as realistic as possible. Since the algorithm proposed by Wang et al. promises good performance for a reasonable set of assumptions, we will study it in great detail in this paper. We attempt to replicate the algorithm and where appropriate, we added in modifications of our own. In this paper, we present algorithms that are modifications to the original algorithm and are necessary to address certain issues that are not mentioned previously. 2 TOPOLOGICAL BOUNDARY RECOGNITION The algorithm proposed by Wang et al. promises good performance for a realistic set of assumptions. The algorithm is distributed and only depends on connectivity information. It is able to create reasonably accurate boundaries with an average node degree of 10. 1

2 There are a total of 6 steps in the algorithm proposed by Wang et al. 1. Create a shortest path tree that is rooted at an arbitrary node. 2. When the shortest path tree is being formed, we find nodes that form the cut where the shortest paths meet after passing around holes. These nodes are found by checking the two criteria that would determine the size of the hole that is to be identified. 3. We take the cut which is furthest from the root and use it form the inner boundary. The inner boundary would encompass all holes in the network and can be found through flooding. 4. After this we will flood the network from the inner boundary. Each node in the network would record its minimum hop count to the boundary and also obtain a label. We will then be able to detect extremal nodes as they are the nodes with the local maximum hop count to the cycle. These extremal nodes would then connect themselves and form extremal connected components (ECC). 5. With the extremal nodes found, we can connect them into a cycle and thus find the outer boundary. Now, if we have started with multiple holes, we can proceed to find other boundaries through the other cuts that exists in the network. 3 OUR CONTRIBUTIONS For our implementation of the algorithm, we adopt the same assumptions that only connectivity information is available to a sensor node and that the actual physical coordinates of the sensor node are not available. In addition, we assume that we have a reliable channel where messages are guaranteed to be delivered within a specified time interval and also an ideal routing protocol that would deliver messages via the shortest path. In order to focus on selected key areas and ensure that we cover them with sufficient depth, we would only be considering the case of a single convex hole in the network. We will focus on three areas in the algorithm by Wang et al., which are the discovery of cut nodes and cut branches, the discovery of extremal nodes and finally, the discovery of the outer boundary. A brief list of the significant areas that we will visit in the paper and improvements that we have implemented is as follows: 1. An improved algorithm for checking criterion 2 2. Creating cut connected components and synchronization prior to creating them 3. Establishing extremal distances and extremal labels 4. Finding extremal nodes and extremal connected components 5. Linking up extremal connected components to form chains 6. Choosing the chains to form the boundary by rejecting false extremal nodes 7. Synchronization required in the algorithm 3.1 Finding the Cut The shortest path tree upon meeting the hole would branch out, and subsequently branches on both side of the hole would meet and form a cut. The nodes on either side of the cut would exchange messages to build the shortest path tree. When they realize that the messages originate from members of the same tree, by comparing their labels, they would check for the first criterion. The first criterion states that their nearest common ancestor (NCA) in the shortest path tree has to be distance away. The distance between two nodes is taken as the hop count between them. This can be done easily by checking the label of the receiver and the label of the 2

3 sender (which would be attached in the message). The second criterion is checked by local flooding from each node in the cut pair up to a distance (Wang et al.,2006). The purpose of the second criterion is to check for branches that run parallel and are not a product of a hole between them and thus ensures that the holes that we detect are of a certain diameter. Since our metric for distance is hop count, and there are no nodes in the hole for us to perform the Original Improved hop count, we have to do local flooding 0 from a branch and attempt to find the other branch. However, as flooding is an expensive operation, we suggest that to check criterion 2, we use only a single node that is of distance up the shortest Ave Node Degree Figure 1 Number of messages sent to check criterion 2. path tree to perform the flooding rather than all nodes in the branch. When the cut nodes are found, we have to connect them into connected components. A problem that we have is that the status of all nodes in the network, as cut or non- cut nodes, are not confirmed at the same time. This is because, it is hard to predict the amount of time required to check the second criterion and a node might have to undergo several checks before it is finally confirmed as a cut node or rejected as a non- cut node. Therefore, at this stage, there is a form of network synchronization that is done at a small and local part of the network. The method that we employ to overcome this problem is based on the fact that when a node has received the shortest path tree message from all its neighbours, it would become stable and not initiate checking for its cut node status. Thus, once a cut node has confirmed its status, it would start to build a connected component rooted No. of messages (in thousands) Figure 2 Extremal nodes are coloured black and examples of ECCs are circled. The arrow indicates increasing extremal labels. at itself. Neighbours would only reply once they are stable. Only the tree rooted at the cut node with the lowest distance to the root would survive and that cut node would realize that the connected component is successfully completed when it receives all replies from its neighbours. We can then synchronize globally to decide which connected component has the greatest distance from the root and build the inner boundary from there. 3.2 Extremal Node Discovery After we have built the inner boundary, we proceed to find extremal nodes. A flooding of the network is done from the inner boundary and each node records the minimum hop count to nodes in the inner boundary (Wang et al., 2006). An extremal node is a node where its neighbours have an extremal distance greater than or equal to its own and it can detect itself by checking its direct neighbours (Wang et al., 2006). Each node would also calculate a label (extremal label) which is the average label of the labels of all its 1 hop neighbours. As 3

4 nodes along the inner boundary would be assigned a unique label which indicates its position (Wang et al., 2006) on the inner boundary, the extremal label of the nodes can provide hints on its position in the network. From Figure 2, we can see that the extremal label increases in the direction of the arrow. Using the similar method for connecting cut nodes, we connect extremal nodes that are in close proximity into extremal connected components (ECC) and these ECC are identified by two nodes which have the greatest distance between each other, or by itself if the ECC consists of only one node. In our implementation, we use the extremal labels to determine which two nodes to select. The node in the ECC with the lowest extremal label would be the head of the ECC and the node with the highest extremal label would be the tail of the ECC. Once all possible ECCs are formed, the network has to be synchronized globally before we can proceed to connect the ECCs together into a boundary. The tail of every ECC would attempt to search for the head of another ECC and would choose the nearest ECC with the highest extremal distance to connect to. We cannot choose any ECC as the ECC might be on the inner boundary or it could be false extremal node. 3.3 Finding the Outer Boundary Finally, we will consider the problem of finding the outer boundary with the use of the connected ECC. In the algorithm by Wang et al., the inner boundary and all its 1-hop neighbours are ignored for this step so that we can differentiate between the inner and outer boundaries (2006). The 2-hop neighbours are then connected to form a path. We experimented with our own modifications for this step. From experiments, we realize that extremal nodes occur at other places other than the boundaries. A node can be out of communication range of the nodes with 1 extremal distance and thus it think that it is an extremal node. We remove these false extremal nodes by selecting the longest connected ECCs that has a head with the highest extremal distance. After selecting appropriate interconnected ECCs, we use the path to control which ECC to choose. All these ECCs have a shortest path to the path for both ends and thus be able to project themselves onto the path. We will then tour the path and reject ECCs that are completely overlapped by other ECCs and those nodes on ECCs that are not rejected would be marked as boundary nodes. 4 IMPLEMENTATION AND EXPERIMENTS We implemented the algorithm with Java because of its object-oriented capabilities. There are two main objects used, the sensors and the messages that are passed between them. All messages are sent to a discrete event simulator (DES) where it is queued and sorted according to time. We start the simulation by adding the message that would trigger the building of the shortest path tree into the DES. The DES would pop the message and would allow a sensor node to act on that message where more messages would be added into DES. The simulation ends when the DES is empty. In our implementation, time is in discrete units and when a node sends a message to a neighbour at time N, the neighbour would receive it at time N+1. In our experiments, we put our algorithms to the test using 3 different datasets and the results are shown below (Figure 3 & 4). First, we have the sensor nodes placed on a grid spaced 0.5 units apart we shift each of them in a random direction by a random amount. The average node degree is 10. Secondly we have the same grid without the random shift and this results in a average node degree of 7. Lastly, we have the sensor nodes placed on a grid spaced 0.45 units apart and we shift each of the nodes by a random amount. It has average node degree of 13. 4

5 (i) (ii) (iii) (iv) (v) (vi) Figure 3 Results for various stages of the algorithm for a network with average node degree of 13 with random shift. (i) The shortest path tree rooted by the node at the top left corner of the network. Cut nodes are coloured cyan. (ii) The inner boundary and extremal distances. The inner boundary is demarcated by the green line and the different colours of the nodes indicate different extremal distances. (iii) The inner boundary and extremal nodes. Extremal nodes are coloured black. (iv) ECC and ECC chains. The head and tail of an ECC is connected with blue lines whereas inter-ecc connection is marked by red lines. (v) The shortest path tree rooted from the inner boundary. (vi) Outer boundary found. Nodes on the outer boundary are marked black. 5

6 5 CONCLUSION In our experiments, we are able to find boundaries that are reasonably close to actual physical boundaries. The algorithm proposed by Wang et al. promises the best performance with a realistic set of assumptions and we try to replicate the algorithm albeit with some modifications of our own. These modifications were added to deal with certain areas that are not addressed by their algorithm. For example, the question of network synchronization and extremal nodes occurring in areas other than the boundary are not discussed in the algorithm. Our paper attempts to solve these problems adequately and efficiently. References [1] Fekete, S. P., Kaufmann, M., Kröller, A., & Lehmann, K. (2005). A New Approach for Boundary Recognition in Geometric Sensor Networks. Proceedings of 17th Canadian Conference on Computational Geometry, (pp ). [2] Fekete, S., Kröller, A., Pfisterer, D., Fischer, S., & Buschmann, C. (2004). Neighbourhood-Based Topology Recognition in Sensor Networks. Proceedings of ALGOSENSORS (pp ). Springer LNCS. Figure 4 Results for average node degree of 10 with random shift (top) and for average node degree of 7 without random shift (bottom) [3] Funke, S. (2005). Topological Hole Detection in Wireless Sensor Networks and its Applications. Proceedings of Joint Workshop on Foundations of Mobile Computing (pp ). Cologne: ACM. [4] Funke, S., & Klein, C. (2006). Hole Dectection or: "How Much Geometry Hides in Connectivity?". Proceedings of 22nd ACM Symposium Computational Geometry (pp ). Sedona: ACM. [5] Kröller, A., Fekete, S. P., Pfisterer, D., & Fischer, S. (2006). Deterministic boundary recognition and topology extraction for large sensor networks. Proceedings of 17th ACM-SIAM Symposium Discrete Algorithms (pp ). Miami: SIAM. [6] Li, M., & Liu, Y. (2007). Rendered Path: Range-Free Localization in Anisotropic Sensor Networks with Holes. Proccedings of ACM MobiCom (pp ). Montreal: ACM. [7] Wang, Y., Gao, J., & Mitchell, J. S. (2006). Boundary Recognition in Sensor Networks by Topological Methods. Proceedings of ACM MobiCom (pp ). Los Angeles: ACM. 6