Energy-efficient routing algorithms for Wireless Sensor Networks Chao Peng Graduate School of Information Science Japan Advanced Institute of Science and Technology March 8, 2007
Presentation Flow Introduction Problem Description System Model Algorithms Performance Comparison Conclusions and Future Work References
Introduction Sensors - small devices with low-power transmissions and energy limitations Ad hoc routing Dynamic topology Transient wireless links and devices Power Anemic, battery lifetime concerns, long life expectancy Communication consumes maximum energy Prior Work: PEGASIS [Step02], LEACH[Wendi00], CCTCCA[Valli03]
Introduction Contd... Constrained resources Limited CPU, battery, and storage Premium communication costs Applications Environmental monitoring Civil structure/earth quake monitoring Premises security Machine instrument diagnosis Health care Crossbow MICAZ mote
Problem Description - Broadcasting There are n nodes in the network Data to be sent from a central node to all other nodes in the network Single Hop or Multi-Hop communication Energy consumed for communication is proportional to distance (, between 2 and 4)[Wendi00] r λ λ Objective # 1: Find a broadcasting tree that consuming minimum energy. Objective # 2: Find a broadcasting tree with maximum lifetime
System Model Assumptions Nodes are static and clocks are synchronized Every node has only one transceiver Each node can adjust its energy level freely A node can transmit or receive at a time but not both There is no need to consider about the interference among the neighboring nodes Communal node Source Sink Shared neighbor Coordinator node Communication border
Energy Model [Wendi00] System Model E total i V i Tx Rx Tx elec amp Rx = elec E E = E + E i E = E k+ k r E = E k λ E elec amp is the electrical energy required on the circuit of transceiver is the amplification energy required to transmit a unit of data over unit distance k is the size of the data packet transmitted by a node r is the distance between communicating nodes
Minimum Energy Broadcasting Tree Building Auxiliary Graph (G -> G ) Sort the reachable neighbor nodes according to the nondecreasing order of the energy-consumption rate (Distance). For each neighbor node, building an auxiliary power node, set the weight of this node as the corresponding energy-consumption Add directed edges from the current node to all its power nodes. If a neighbor node can be connected by a certain energy level, add a directed edge from the corresponding power node to that neighbor node. Set the weight of each edge as zero.
Auxiliary Graph MEBT (2) s s a b c d s a b c d a b c d
MEBT (3) Node Weighted Steiner Tree Problem Undirected graph G=(V,E), weight w(v) for each node v, a set of Steiner nodes R in V. We are asked to find a tree T for G such that all nodes in R are connected by T and the sum of the weights of the nodes in T is minimized. This problem is NP-Hard, but there exists a O(log V )- approximation algorithm for it. Using the algorithm for the above NWST Problem We can let the set of nodes V in the original graph G to be the set of Steiner nodes R in G. Then the Minimum Energy Broadcasting Tree problem is same to the directed version of the NWST problem.
MEBT (4) Outline of the algorithm for the above NWST Problem Starting from the source node, we use a greedy policy to connect a set of isolated nodes which is "optimal" in each iteration according to the average cost, thus by less than n iterations we can connect all nodes in the graph.
MEBT (5) The Algorithm for Computing the Minimum Energy Broadcasting Tree Step 1: Given a graph G=(V,E), building the corresponding auxiliary graph. Step 2: Call the program for the NWST Problem to find the Minimum-cost Node Weighted Steiner Tree. Step 3: Mark the non-leaf nodes of the computed tree in the original graph. Step 4: For each marked node, try to convert itself to another non-offspring neighboring marked node to gain a total energy decreasing. Step 5: For the remainder nodes, try to connect itself to the nearest marked node.
Maximum Lifetime Broadcasting Tree In some critical missions, we need to find a broadcasting tree that can perform the datatransfer for a long period without any interruption. In such occasions we need to guarantee that each node in the broadcasting tree will have enough energy during the mission. The Minimum Energy Broadcasting Tree might be very short-lived because some node which has remote children may consume its energy too quick. Thus we need to find new algorithms for this problem.
MLBT (2) Unlike the previous NP-Complete problem, this MLBT problem is in P. For each node, if its energy-consumption rate and its residual energy value are known, then we can compute its life-span. If there is a life-time requirement for a given mission, we can simply remove the edges with a lower life-span and find a broadcasting tree in the remainder graph. If we want to find the maximum possible life time, we can perform binary search on the life-span range.
MLBT (3) The Algorithm for Computing the Maximum Lifetime Broadcasting Tree Step 1: Given a graph G=(V,E), turn it into a directed graph and compute the life-span of each edge. Step 2: Do binary search on the life-span range. For each value, using the breadth-first search algorithm to check whether the graph is still connected. Step 3: After we finally narrow down the range and find the maximum life-span bound, remove all edges with a value less than this bound. Step 4: Call the previous algorithm to compute a minimum energy broadcasting tree in the remainder graph.
Performance Comparison Since Most Algorithms focus on Computing the Minimum Energy Broadcasting Tree, we compare the performance of our first algorithm with them. We use c language and mat-lab to do the simulation. The parameters used in our simulations follows those in existing publications. The number of nodes n is always 60 and nodes are static. The maximum communication radius r is fixed to 5*50 meters. Nodes are uniformly distributed in a square area with randomly assigned energy unit, ranging from 800mw to 8000mw. We repeat 50 rounds, in each round the source node will start a session lasts 2 minutes.
Performance Comparison (2) (A) The topology graph of a MANET
Performance Comparison (3) (B) The Minimum Spanning Tree
Performance Comparison (4) (C) The Shortest Path Tree
Performance Comparison (5) (D) The WNE Algorithm Tree
Performance Comparison (6) (E) The Tree Computed by Our Algorithm
Performance Comparison (7) (F) The Disk Coverage Graph
Performance Comparison (8) Min Value Max Value Average (mw) (mw) (mw) MST 957 2932 1218 SPT 922 3235 1026 WNE 754 2109 927 This paper 581 2238 875
Conclusions and Future Work Proposed an approximation algorithm for computing Minimum Energy Broadcasting Tree with guaranteed performance. Proposed an exact algorithm for computing Maximum Lifetime Broadcasting Tree. Future simulation should be performed on real test-bed. Extend our algorithm to solve other similar problems such as the converge-cast issue.
References [Valli03] V. Annamalai., S.K.S. Gupta and L. Schwiebert On Tree- Based Convergecasting in Wireless Sensor Networks. IEEE Wireless Communications and Networking Conference 2003, New Orleans 2003. [Imrich87] I. Chalmatac. and S. Kutten Tree-Based Broadcasting in Multihop Radio Networks. IEEE Transactions on Computers Vol. C-36, No. 10, Oct 1987. [Wendi00] W. R. Heinzelman, A. Chandrakasan and H. Balakrishnan Energy-Efficient Communication Protocol for Wireless Micro Sensor Networks. Proceedingsof the Hawaii International Conference on System Science, Jan 2000.
Reference [Step02] S. Lindsey, C. Raghavendra, K. M. Sivalingam Data Gathering Algorithms in Sensor Networks Using Energy Metrics. IEEE Transactions on Parallel and Distributed Systems, Vol. 13, No. 9, Sept 2002. [Bhas02] B. Krishnamachari, D. Estrin and S. Wicker Impact of Data Aggregation in Wireless Sensor Networks. International Workshop on Distributed Event-Based Systems (DEBS, 02) Vienna, Austria, July 2002. [WNE00] J.E. Wieselthier, G.D. Nguyen, and A. Ephremides, On Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks, in Proc. INFOCOM 00, 2000.