A branch‐and‐price algorithm for the rainbow cycle cover problems

Abstract

AbstractA rainbow cycle in an undirected edge‐colored graph is a cycle in which all edges have different colors. A rainbow cycle cover of a graph is a set of disjoint rainbow cycles, where each vertex belongs to exactly one cycle. The objective of the rainbow cycle cover problem is to minimize the number of rainbow cycles used to cover the vertices of the graph while the trivial cycle version also keeps the number of isolated vertices (called trivial rainbow cycles) at minimum. We present a branch‐and‐price procedure with column generation to solve both versions of the rainbow cycle cover problem. We compare our results with the literature in terms of computational performance. We also discuss two approaches to possibly improve the performance of the branch‐and‐price procedure.