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 log n) per query pair (p, q). In this paper we relax the exactness requirement and only compute approximate (1 +ε) solutions which allows us to guarantee constant query time using linear space and O(n log n) preprocessing time. The dependence on e is polynomial in 1/ε. One tool we employ might be of independent interest: For any pair of points (p, q) ∈ P is contained in Z~2 we can report in constant time the cluster pair (A, B) representing (p, q) in a well-separated pair decomposition of P.
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