Benchmarks for Strictly Fundamental Cycle Bases

In the Minimum Strictly Fundamental Cycle Basis (MSFCB) problem one is looking for a spanning tree such that the sum of the lengths of its induced fundamental circuits is minimum. We identify square planar grid graphs as being very challenging testbeds for the MSFCB. The best lower and upper bounds for this problem are due to Alon, Karp, Peleg, and West (1995) and to Amaldi et al. (2004). We improve their bounds significantly, both empirically and asymptotically. Ideally, these new benchmarks will serve as a reference for the performance of any new heuristic for the MSFCB problem.