Connectivity and Scheduling in Wireless Sensor Networks Youn-Hee Han yhhan@kut.ac.kr Korea University of Technology and Education Internet Computing Laboratory http://icl.kut.ac.kr

Connectivity

Connectivity Why Connectivity? Any sensing data should be sent to gateway (sink, base station) node Multi-hop routing Base Station Sink

K-Connectivity Connected Graph of Sensor Networks Vertex: each sensor nodes Edge: direct communication path for pairs of sensors there exists an edge between two vertices iff the distance between them is less or equal to the transmission range r.

K-Connectivity [Definition] k-connectivity The network will remain connected after removing any arbitrary k-1 sensors from network. It is also called “vertex k-connectivity” (not “edge k-connectivity”) k-connected:  any pair of nodes are connected by k indep. paths Independent paths:

K-Connectivity Examples 2-connected 4-connected

K-Edge-Connectivity [Definition] k-edge-connectivity The network will remain connected after removing any arbitrary k-1 edges from network. k-edge-connected:  any pair of nodes are connected by k disjoint paths disjoint paths:

Min-Power Connectivity Problem Connectivity & Transmission Power Nodes in the network correspond to transmitters More power  larger transmission range  More Edges  More Connectivity transmitting to distance r requires r power Battery operated  power conservation critical [Definition] Min-Power Connectivity Problems Find min-power range assignment so that the resulting communication network satisfies prescribed properties (k-connectivity)

Min-Power Connectivity Problem a c d g f e a b d g f e c Range assignment Communication network

K-Connectivity & K-Coverage Relation between K-Coverage and K-Connectivity [3] Communication Range: Sensing Range: [Theorem] If the given region is continuous and , “The region is k-covered” means “The region is k-connected” For example, k=1 Assume that the requested coverage level, k, is one and If The sensors covers the whole region completely, then Any sensing data produced by a sensor can be delivered to the sink node.

Sensing and Communication Ranges Real Products’ Ranges [7]

Coverage and Surveillance Path [Voronoi Diagram Tutorial] http://nms.lcs.mit.edu/~aklmiu/6.838/L7.pdf

Voronoi diagram Voronoi diagram [8] The Voronoi diagram is formed from lines that bisect and are perpendicular to the lines that connect two neighboring sensors. Each point s has a Voronoi cell V(s) consisting of all points closer to s than to any other point

Voronoi diagram Voronoi diagram examples 1 point 2 points form “a perpendicular bisector”

Voronoi diagram Voronoi diagram examples Collinear points form “a series of parallel lines”

Voronoi diagram Voronoi diagram examples Non-collinear points form “Voronoi half lines” that meet at a vertex

Voronoi diagram Voronoi cells and segments Which of the following is true for 2-D Voronoi diagrams? Four or more non-collinear pointss are… 1) sufficient to create a bounded cell 2) necessary to create a bounded cell 3) 1 and 2 4) none of above Four points’ degenerate case of bounded cell:

Property I of Voronoi diagram

Property II of Voronoi diagram

Surveillance Path Maximal Breach Path [8] Voronoi Path (= Maximal Breach Path) The path where the surveillance level is the lowest The path where its closest distance to any sensor is as large as possible. Voronoi Path (Edge) Voronoi diagram Voronoi Partition

Surveillance Path Maximal Support Path [8] Delaunay Triangulation Path (= Maximal Support Path) The path where the surveillance level is the lowest The path where its closest distance to any sensor is as short as possible. Delaunay triangulation

Coverage and Scheduling

Scheduling Basic Policy Sensor should be active or sleep? Scheduling (related to the coverage issue) An interval: is active Another interval: is active So, the battery power can be saved

Scheduling Scheduling Type Centralized Distributed All sensors send “their location information” to the centralized sink node. The sink node performs “its scheduling algorithm” for the sensors The sink node broadcasts “the scheduling information” to all sensor nodes Each sensor becomes active or sleep according to the information Distributed Each sensor self-determies its scheduling time # of messages reduced

Centralized Scheduling MDSC (Maximum Disjoint Set Covers) [9] [Definition] Maximum Disjoint Set Covers Problem

Centralized Scheduling MDSC (Maximum Disjoint Set Covers) [9] For example, C={S1, S2, S3, S4}, TARGETS={t1, t2, t3} A sensor’s battery lifetime: 1 Network Lifetime without any scheduling: 1 By MDSC Scheduling Two Set Covers, C1 and C2 C1={S1, S2} with active time=1 C1={S3, S4} with active time=1 So that, network lifetime: 2 s2 s1 s4 s3 t3 t1 t2 s1 s2 s3 s4 t3 t2 t1

Centralized Scheduling MSC (Maximum Set Covers) [10] [Definition] Maximum Set Covers Problem removed! MSC MDSC MDSC problem is a special case of MSC problem.!

Centralized Scheduling MSC (Maximum Set Covers) [10] For Example, By MSC Scheduling Network Lifetime: 2.5 s2 s1 s4 s3 t3 t1 t2 active time=0.5 active time=0.5 active time=0.5 active time=1

Centralized Scheduling Integer Programming Formulation of the MSC Problem [10]

Centralized Scheduling Integer Programming Formulation of the MSC Problem [10]

Centralized Scheduling Integer Programming  Linear Programming

Centralized Scheduling MSC (Maximum Set Covers) [10, 11] Existing Algorithms Linear Programming [10] Greedy [10] (Complexity: ) Branch-and-Bound [11] i: # of set covers, m: # of targets, n: # of sensors

Centralized Scheduling MSC (Maximum Set Covers) [10, 11] Existing Algorithms Linear Programming [10] Greedy [10] (Complexity: ) Branch-and-Bound [11] i: # of set covers, m: # of targets, n: # of sensors

Distributed Scheduling 1-Coverage Preserving Scheduling (1-CP) [12] For Example Init Phase: 1) Each sensor exchange its location and Ref. value 2) Each sensor get its schedule (active) time The set of intersection points within ‘s area Trnd=20 The set of sensors covering the target p Ref1=2, Ref2=9, Ref3=11

Distributed Scheduling 1-Coverage Preserving Scheduling (1-CP) [12] 2 16.5 5.5 11 9

References C.-F. Huang and Y.-C. Tseng, The Coverage Problem in a Wireless Sensor Network, In ACM International Workshop on Wireless Sensor Networks and Applications (WSNA), pp. 115–121, 2003. N. Ahmed, S. S. Kanhere and S. Jha, Probabilistic Coverage in Wireless Sensor Networks, in Proceedings of the IEEE Workshop on Wireless Local Networks (WLN, in conjunction with LCN 2005) , Sydney, Australia, pp. 672-679, November 2005. X. Wang, G. Xing, Y. Zhang, C. Lu, R. Pless, and C. Gill, Integrated coverage and connectivity configuration in wireless sensor networks, In ACM International Conf. on Embedded Networked Sensor Systems (SenSys), pp. 28–39, 2003. C.-F. Huang, Y.-C. Tseng, and L.-C. Lo, The Coverage Problem in Three-Dimensional Wireless Sensor Networks, Journal of Interconnection Networks, Vol. 8, No. 3, pp. 209-227. Sep. 2007. Y. Zou and K. Chakrabarty, "Sensor deployment and target localization based on virtual forces," in Proceedings of INFOCOM 2003, March 2003. S.-P. Kuo, Y.-C. Tseng, F.-J. Wu, and C.-Y. Lin, A Probabilistic Signal-Strength-Based Evaluation Methodology for Sensor Network Deployment, International Journal of Ad Hoc and Ubiquitous Computing, Vol. 1, No. 1-2, pp. 3-12, 2005 36/37

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