A combinatorial algorithm for the determinant
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
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
On the approximability of minmax (regret) network optimization problems
Information Processing Letters
The complexity of bottleneck labeled graph problems
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
An s-t connection problem with adaptability
Discrete Applied Mathematics
Approximating min-max (regret) versions of some polynomial problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
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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This paper investigates, for the first time in the literature, the approximation of min-max (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack. For a bounded number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between multi-objective and min-max optimization. Using dynamic programming and classical trimming techniques, we construct a fully polynomial-time approximation scheme for min-max regret shortest path. We also establish a fully polynomial-time approximation scheme for min-max regret spanning tree and prove that min-max regret knapsack is not at all approximable. We also investigate the case of an unbounded number of scenarios, for which min-max and min-max regret versions of polynomial-time solvable problems usually become strongly NP-hard. In this setting, non-approximability results are provided for min-max (regret) versions of shortest path and spanning tree.