Efficient Spanner Construction for Directed Transmission Graphs ∗
نویسندگان
چکیده
Let P ⊂ R be a set of n points, each with an associated radius rp > 0. The transmission graph G for P has vertex set P and a directed edge from p to q if and only if q lies in the ball with radius rp around p. Let t > 1. A t-spanner H for G is a sparse subgraph such that for any two vertices p and q connected by a path of length l in G, there is a path of length at most t · l from p to q in H. Given G implicitly as points with radii, we show how to compute a t-spanner for G in time O(n(log n+ log Ψ)), where Ψ is the ratio of the largest and smallest radius in P .
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