Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Cardinality constrained and multicriteria (multi)cut problems
Journal of Discrete Algorithms
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
Complexity of the min-max (regret) versions of min cut problems
Discrete Optimization
Stochastic combinatorial optimization via poisson approximation
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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 _emphiall_/emph the k costs associated with it. In the OR-version, an edge can be purchased by paying erbany oneerb 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.