Fast Approximation Algorithm for Maximum Lifetime Aggregation Trees in Wireless Sensor Networks

Abstract

O ne ultimate goal of wireless sensor networks is to collect the sensed data from a set of sensors and transmit them to some sink node via a data gathering tree. In this work, we are interested in data aggregation, where the sink node wants to know the value for a certain function of all sensed data, such as minimum, maximum, average, and summation. Given a data aggregation tree, sensors receive messages from children periodically, merge them with its own packet, and send the new packet to its parent. The problem of finding an aggregation tree with the maximum lifetime has been proved to be NP-hard and can be generalized to finding a spanning tree with the minimum maximum vertex load, where the load of a vertex is a nondecreasing function of its degree in the tree. Although there is a rich body of research in those problems, they either fail to meet a theoretical bound or need high running time. In this paper, we develop a novel algorithm with provable performance bounds for the generalized problem. We show that the running time of our algorithm is in the order of O mn m n , where m is the number of edges, n is the number of sensors, and is the inverse Ackerman function. Though our work is motivated by applications in sensor networks, the proposed algorithm is general enough to handle a wide range of degree-oriented spanning tree problems, including bounded degree spanning tree problem and minimum degree spanning tree problem. When applied to these problems, it incurs a lower computational cost in comparison to existing methods. Simulation results validate our theoretical analysis.

Speeding Up Exact Algorithms for Maximizing Lifetime of WSNs Using Multiple Cores

“…Unfortunately, it is NP-hard in most scenarios when nodes can or cannot perform data aggregation. Researchers resort to polynomial-time approximation algorithms by sacrificing accuracy (e.g., [8]), or exponential-time exact algorithms by sacrificing running time (e.g., [1,3]). While both algorithms have important applications, we focus on exact algorithms in this paper.…”

“…← \ { }; (8) reverse the direction of edges in , and perform a breadth-first search from the sink; Different from Algorithm 2, we need to verify whether the constructed subproblem is feasible. This is done by reversing the directions of the edges and performing a breadth-first search from the sink in line (8).…”

“…This is done by reversing the directions of the edges and performing a breadth-first search from the sink in line (8). The subproblem is feasible if and only if all vertices are visited.…”

“…reverse the directions of edges in and perform a breadth-first search from the sink (8) if all vertices are visited then (9) construct subproblem with as the network; (10) include to ; (11) return ; Algorithm 4: decomp fixing parent.…”

“…This is in line with intuition since all CPU cores are used. Second, when the number of subproblems is either small (8) or large (20), the average running time is not the smallest. We get smaller running time when the number of subproblems is 12 or 16.…”