Broadcast with Hitch-hiking in Wireless Ad-Hoc Networks (Invited Talk Abstract)

Summary form only given. There have been papers indicating that the maximal ratio combiner device can result in energy savings in wireless ad hoc networks by using hitch-hiking. We study the min-energy broadcast with hitch-hiking problem, an idealized version of broadcast using hitch-hiking, a problem studied experimentally in the INFOCOM 2004 paper of Agarwal et al. min-energy broadcast with hitch-hiking captures the maximum savings one can achieve in broadcasting using maximal ratio combiners. We show that the optimum of the classical min-energy broadcast problem is at most O(log² n) times the optimum of min-energy broadcast with hitch-hiking, where n is the number of nodes in the networks. We show that this bound is tight up to a constant. Moreover, the same bounds hold for Unicast. In the special case when the nodes are on a line and the power requirement for node u to reach node v is d(u, v)^K, where d(u, v) the Euclidean distance between u and v and k is the signal attenuation exponent, which is assumed to be in between 2 and 5, we show that the optimum of the min-energy broadcast problem is at most a constant times optimum of min-energy broadcast with hitch-hiking. A formal definition of min-energy broadcast with hitch-hiking is given below. The input consists of a complete directed graph G = (V, E) with power requirement function c : E rarr R⁺ , and a source s epsi V. The output consists of a permutation tau =< v₁, v₂, ..., v _n > of V with v_n = s and power assignment p(v) of every vertex v. For every 1 les i les i < j les n, define q(v_i, v_j ) = p(v_i)/c(v_i)_j). An output is feasible if for every j > 1 we have Sigma_{i = 1} ^{j - 1} q(v_iv_j) ges 1. The objective is to minimize Sigma_{i = 1} ⁿ p(v_i)