Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Algorithms for Generating Fundamental Cycles in a Graph
ACM Transactions on Mathematical Software (TOMS)
An algorithm for finding a fundamental set of cycles of a graph
Communications of the ACM
Algorithms for finding a fundamental set of cycles for an undirected linear graph
Communications of the ACM
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Minimum cut bases in undirected networks
Discrete Applied Mathematics
Integral cycle bases for cyclic timetabling
Discrete Optimization
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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.