Abstract
We consider two multicriteria versions of the global minimum cut problem in undirected graphs. In the k-criteria setting, each edge of the input graph has k non-negative costs associated with it. These costs are measured in separate, non interchangeable, units. In the AND-version of the problem, purchasing an edge requires the payment of all the k costs associated with it. In the OR-version, an edge can be purchased by paying any one of the k-costs associated with it. Given k bounds b 1,b 2,...,b k , the basic multicriteria decision problem is whether there exists a cut C of the graph that can be purchased using a budget of b i units of the i-th criterion, for 1≤ i≤ k.
We show that the AND-version of the multicriteria global minimum cut problem is polynomial for any fixed number k of criteria. The OR-version of the problem, on the other hand, is NP-hard even for k=2, but can be solved in pseudo-polynomial time for any fixed number k of criteria. It also admits an FPTAS. Further extensions, some applications, and multicriteria versions of two other optimization problems are also discussed.
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Armon, A., Zwick, U. (2004). Multicriteria Global Minimum Cuts. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_8
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DOI: https://doi.org/10.1007/978-3-540-30551-4_8
Publisher Name: Springer, Berlin, Heidelberg
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