Computational comparison of several greedy algorithms for the minimum cost perfect matching problem on large graphs

The aim of this paper is to computationally compare several algorithms for the Minimum Cost Perfect Matching Problem on an undirected complete graph. Our work is motivated by the need to solve large instances of the Capacitated Arc Routing Problem (CARP) arising in the optimization of garbage collection in Denmark. Common heuristics for the CARP involve the optimal matching of the odd-degree nodes of a graph. The algorithms used in the comparison include the CPLEX solution of an exact formulation, the LEDA matching algorithm, a recent implementation of the Blossom algorithm, as well as six constructive heuristics. Our results show that two of the constructive heuristics consistently exhibit the best behavior compared with the other four.