The minimum risk spanning tree problem

Abstract

This paper studies a spanning tree problem with interval data that finds diverse applications in network design. Given an underlying network G = (V, E), each link e ∈ E can be established by paying a cost ce ∈ [c-e c̄e], and accordingly takes a risk c̄e - ce/c̄e - ceof link failure. The minimum risk spanning tree (MRST) problem is to establish a spanning tree in G of total cost no more than a given constant so that the risk sum over the links on the spanning tree is minimized. In this paper, we propose an exact algorithm for the MRST problem that has time-complexity of O(m 2 log m log n(m + n log n)), where m = |E| and n= |V|. © Springer-Verlag Berlin Heidelberg 2007.