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General approximation schemes for min–max (regret) versions of some (pseudo-)polynomial problems

Aissi, Hassene; Bazgan, Cristina; Vanderpooten, Daniel (2010), General approximation schemes for min–max (regret) versions of some (pseudo-)polynomial problems, Discrete Optimization, 7, 3, p. 136-148. http://dx.doi.org/10.1016/j.disopt.2010.03.004

Type
Article accepté pour publication ou publié
Date
2010
Journal name
Discrete Optimization
Volume
7
Number
3
Publisher
Elsevier
Pages
136-148
Publication identifier
Metadata
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Author(s)
Aissi, Hassene

Bazgan, Cristina

Vanderpooten, Daniel
Abstract (EN)
While the complexity of min–max and min–max regret versions of most classical combinatorial optimization problems has been thoroughly investigated, there are very few studies about their approximation. For a bounded number of scenarios, we establish general approximation schemes which can be used for min–max and min–max regret versions of some polynomial or pseudo-polynomial problems. Applying these schemes to shortest path, minimum spanning tree, minimum weighted perfect matching on planar graphs, and knapsack problems, we obtain fully polynomial-time approximation schemes with better running times than the ones previously presented in the literature.
Subjects / Keywords
Knapsack; Minimum spanning tree; Min–max regret; Fptas; Min–max; Shortest path; Minimum weighted perfect matching; Approximation