TY - JOUR

T1 - Multicriteria global minimum cuts

AU - Armon, Amitai

AU - Zwick, Uri

PY - 2006/9

Y1 - 2006/9

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 ith 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 ith 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.

KW - Graph algorithms

KW - Minimum cut

KW - Multicriteria optimization

UR - http://www.scopus.com/inward/record.url?scp=33747894607&partnerID=8YFLogxK

U2 - 10.1007/s00453-006-0068-x

DO - 10.1007/s00453-006-0068-x

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AN - SCOPUS:33747894607

SN - 0178-4617

VL - 46

SP - 15

EP - 26

JO - Algorithmica

JF - Algorithmica

IS - 1

ER -