Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
A new approach to the minimum cut problem
Journal of the ACM (JACM)
Computing All Small Cuts in an Undirected Network
SIAM Journal on Discrete Mathematics
Journal of the ACM (JACM)
Improved approximation schemes for scheduling unrelated parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Random Sampling in Cut, Flow, and Network Design Problems
Mathematics of Operations Research
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Minimum cuts in near-linear time
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A New Algorithm for Multi-objective Graph Partitioning
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Cardinality constrained minimum cut problems: complexity and algorithms
Discrete Applied Mathematics
Multicriteria Optimization
A fully polynomial bicriteria approximation scheme for the constrained spanning tree problem
Operations Research Letters
Complexity of the min-max (regret) versions of cut problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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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.