Approximating Energy Efficient Paths in Wireless Multi-hop Networks

Given the positions of n sites in a radio network we consider the problem of finding routes between any pair of sites that minimize energy consumption and do not use more than some constant number k of hops. Known exact algorithms for this problem required Ω(n logn) per query pair (p, q). In this paper we relax the exactness requirement and only compute approximate (1+2) solutions which allows us to guarantee constant query time using linear space and O(n logn) preprocessing time. The dependence on 2 is polynomial in 1/2. One tool we employ might be of independent interest: For any pair of points (p, q) ∈ P ⊆ Z we can report in constant time the cluster pair (A,B) representing (p, q) in a well-separated pair decomposition of P .