Algorithms for the Ring Star Problem

Abstract

We address the Ring Star Problem (RSP) on a complete graph \(G=(V,E)\) whose edges are associated with both a nonnegative ring cost and a nonnegative assignment cost. The RSP is to locate a simple ring (cycle) R in G with the objective of minimizing the sum of two costs: the ring cost of (all edges in) R and the assignment cost for attaching nodes in \(V\setminus V(R)\) to their closest ring nodes (in R). We focus on the metric RSP with fixed edge-cost ratio, in which both ring cost function and assignment cost function defined on E satisfy triangle inequalities, and the ratios between the ring cost and assignment cost are the same value \(M\ge 1\) for all edges.