Priority Based Enhancement of Online Power-Aware Routing in Wireless Sensor Network. Ronit Nossenson Jerusalem College of Technology

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1 Priority Based Enhancement of Online Power-Aware Routing in Wireless Sensor Network Ronit Nossenson Jerusalem College of Technology COMCAS

2 What are sensor networks? Infrastructure-less networks Typically connects a large number of small static nodes capable of: Sensing Processing information Storing information Wireless communication Limited power Power Aware routing Ronit Nossenson COMCAS

3 The goal To maximize the network lifetime of on-line power-aware routing algorithm The lifetime of a network with respect to a sequence of messages is the earliest time when a message cannot be sent due to saturated nodes NP-hard problem [Li, Aslam, Rus]: no on-line routing algorithm has a constant competitive ratio in terms of the lifetime of the network Ronit Nossenson COMCAS

4 The optimization problem Let m 1, m 2, be a sequence of messages to be delivered between nodes in the network (on-line routing) We wish to: Maximize the number of delivered messages in the system Subject To: (1) message m s from v i to v j can be delivered iff a) m 1,, m s-1 are successfully delivered; and b) There exists at least one path from v i to v j with enough power to deliver the message m s (2) the total power used to send all messages from node v i does not exceed the initial power of v i Ronit Nossenson COMCAS

5 The means Priority based enhancement to on-line power - aware routing algorithms The node priority assignment is driven from the network connectivity model It represents the importance of the node in the network topology structure Ronit Nossenson COMCAS

6 The induced graph A vertex: a node An edge: a wireless link A vertex weight: the node's power level (finite) An edge weight: the power cost of sending a unit message (w = kd c ) Ronit Nossenson COMCAS

7 Connectivity definitions (1/2) Let G(V,E) be an undirected connected graph A minimal edge-cut C of G is an edge set whose removal disconnects G and removal of any proper part of C does not disconnect G If C = k then C is called a k-cut, 1-cut is also called a bridge Ronit Nossenson COMCAS

8 Connectivity definitions (2/2) Two vertices {u,v} are called k-connected if no k'-cut, k' < k, separates u from v The equivalence classes of this relation are called k-classes The partition of V into the (k+1)-classes is a refinement of the partition of V into k-classes. Thus, the connectivity classes have a hierarchical structure Example: {1,2,3,4,5,6} are in the same 2-class; This 2-class is divided into three 3-classes: {1,2,4,5}, {3}, and {6} Ronit Nossenson COMCAS

9 Connectivity models (1/3) For a k-connected graph, its connectivity model represents both its (k+1)-classes and its k-cuts The well known bridge-tree model of a 1-connected graph represents its bridges and its 2-classes [Westbrook and Tarjan] Ronit Nossenson COMCAS

10 Connectivity models (2/3) The cycle-tree model of a 2-connected graph represents its 2-cuts and its 3-classes [Galil and Italiano] Cycle-tree = each edge participates in one cycle the number of edges is O( V ) v 1 v 2 a) The induced graph v ={v 1,v 2 } b) The cycle-tree Ronit Nossenson COMCAS

11 Connectivity models (3/3) These connectivity models are, in fact, special cases of a more general cactus-tree model [Dinic, Karzanov and Lomonosov] We use: the bridge-tree and the cycle-tree This connectivity model represents two levels of connectivity the 1-classes, their partition refinement of 2-classes, the 1-cuts and the 2-cuts A special case of the two-level cactus-tree model of [Dinitz and Nutov] Ronit Nossenson COMCAS

12 Example Important observation: edges of this connectivity model are real network edges! Ronit Nossenson COMCAS

13 The priority enhancement (1/2) Vertex which is attached to a bridge receives the highest priority (red color) Vertex which is attached to an edge from the cycletree receives a medium priority level (yellow color) Others receive low priority (green color) Ronit Nossenson COMCAS

14 The priority enhancement (2/2) The routing algorithm prefers paths with low priority nodes (a to b) Initial power assignment according to nodes priority Ronit Nossenson COMCAS

15 Connectivity models references E. A. Dinic, A. V. Karzanov and M. V. Lomonosov, On the structure of the system of minimum edge cuts in a graph Ye. Dinitz and Z. Nutov, A 2-level cactus tree model Z. Galil and G. F. Italiano, Maintaining the 3- edge-connected components of a graph on line J. Westbrook and R. E. Tarjan, Maintaining bridge-connected and bi-connected components on line Ronit Nossenson COMCAS

16 Questions? Ronit Nossenson COMCAS