University of Twente, Department of Applied Mathematics
Abstract
We present an average case analysis of the minimum spanning tree heuristic for the range assignment problem on a graph with power weighted edges. It is well-known that the worst-case approximation ratio of this heuristic is 2. Our analysis yields the following results: (1) In the one dimensional case (d=1), where the weights of the edges are 1 with probability p and 0 otherwise, the average-case approximation ratio is bounded from above by 2−p. (2) When d=1 and the distance between neighboring vertices is drawn from a uniform [0,1]-distribution, the average approximation ratio is bounded from above by 2−2−α where α denotes the distance power radient. (3) In Euclidean 2-dimensional space, with distance power gradient α=2, the average performance ratio is bounded from above by 1+log2