The minimum fundamental cycle basis problem: a new heuristic based on edge swaps

This paper describes a new heuristic method for finding minimum fundamental cycle bases in biconnected, undirected graphs. At each iteration, a particular edge swap is applied to the spanning tree corresponding to the current fundamental cycle basis is computed. Our numerical experiments, obtained for square mesh graphs, show that this heuristic finds fundamental cycle bases with considerably lower costs compared to other available heuristics.