Daniel Berend
ABSTRACT
The temporary and unfixed physical topology of a wireless adhoc network is determined by the distribution of the wireless nodes as well as the transmission power (range) assignment of each node. This paper studies asymmetric power assignments for which the induced communication graph is k-strongly connected, while minimizing the total energy assigned (which is NP-Hard) and maximizing the network lifetime. We show that our power assignment algorithm from [9] achieves a bicriteria approximation of (O(k),O(k log n k√nφ(n))) with high probability for the minimal total cost/maximal network (respectively) lifetime problem in the plane in the case of arbitrary battery charges. The same algorithm is an (O(k),O(1))-approximation in the case of uniform batteries. To the best of our knowledge, this is the first attempt to provide a bicriteria approximation factor for the total power assignment cost and the network lifetime under the k-fault resilience criterion. We provide some results for the linear power assignment algorithm in [30] as well. In addition, we extend the static algorithms above to support dynamic node insert/delete operations in O(log n) time for the linear case and an expected O(k poly log n) amortized time in the plane.
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Index Terms
- Power efficient resilience and lifetime in wireless ad-hoc networks
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Reviews
Feodor F. Dragan
One of the fundamental problems in wireless ad hoc networks is finding a power assignment to induce a communication graph that satisfies some topology property. Two natural optimization objectives arise: minimizing the total energy consumption and maximizing the network lifetime. This paper examines this problem under the asymmetric model-that is, the communication graph is directed. It is a bicriteria optimization problem; the exact problem formulation is as follows: Assume a set of n transceivers = t1, ... , tn is positioned in the plane R2. Each t __?__ has initial battery charge b(t) = 0. Given an integer k = 1 and a real number α __?__ [2,4], one needs to assign to each t __?__ a transmission power p(t) = 0 so that: the resulting directed communication graph H:=( , ), where :=(s, t): p(s) = dα(s, t), is a k-fault resistant strongly connected graph; the total power assigned is minimized; and the network lifetime is maximized. Berend et al. analyze their previously published static algorithms for k-strong connectivity [1,2], showing that in addition to provable approximation bounds for the total energy consumption, their algorithms also produce a good approximation factor for the maximal network lifetime. For example, the algorithm from Carmi et al. [1] produces a solution with the total power at most O(k) × (minimum total power) and with the network lifetime at least × (maximum lifetime), with high probability in the case of variable battery charges. The same algorithm produces a solution with the network lifetime at least × (maximum lifetime) in the case of uniform batteries. They also show that if the problem is restricted to R1, then even better approximation bounds can be achieved. In addition, this paper extends the algorithms from Carmi et al. [1] and Shpungin [2] to support dynamic node insert/delete operations with an expected O(k poly log n) amortized cost. This is the first paper to provide a bicriteria approximation factor for the total power assignment cost and the network lifetime under the k-fault resilience criterion. Online Computing Reviews Service
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