Abstract
The problem of finding a fundamental cycle basis with minimum total cost in a graph is NP-hard. Since fundamental cycle bases correspond to spanning trees, we propose new heuristics (local search and metaheuristics) in which edge swaps are iteratively applied to a current spanning tree. Structural properties that make the heuristics efficient are established. We also present a mixed integer programming formulation of the problem whose linear relaxation yields tighter lower bounds than known formulations. Computational results obtained with our algorithms are compared with those from existing constructive heuristics on several types of graphs.
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Amaldi, E., Liberti, L., Maculan, N., Maffioli, F. (2004). Efficient Edge-Swapping Heuristics for Finding Minimum Fundamental Cycle Bases. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_2
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DOI: https://doi.org/10.1007/978-3-540-24838-5_2
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