TY - JOUR

T1 - Multicriteria global minimum cuts

AU - Armon, Amitai

AU - Zwick, Uri

PY - 2004

Y1 - 2004

N2 - 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 b1, b2,..., bk, the basic multicriteria decision problem is whether there exists a cut C of the graph that can be purchased using a budget of bi 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.

AB - 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 b1, b2,..., bk, the basic multicriteria decision problem is whether there exists a cut C of the graph that can be purchased using a budget of bi 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.

UR - http://www.scopus.com/inward/record.url?scp=35048867417&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-30551-4_8

DO - 10.1007/978-3-540-30551-4_8

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AN - SCOPUS:35048867417

SN - 0302-9743

VL - 3341

SP - 65

EP - 76

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -