Result: Approximation complexity of min-max (regret) versions of shortest path, spanning tree, and knapsack

Title:
Approximation complexity of min-max (regret) versions of shortest path, spanning tree, and knapsack
Authors:
AISSI, Hassene, BAZGAN, Cristina, VANDERPOOTEN, Daniel
Source:
Algorithms - ESA 2005 (13th annual European sympoisum, Palma de Mallorca, Sapin, October 3-6, 2005, proceedings)Lecture notes in computer science. :862-873
Publisher Information:
New York, NY: Springer, 2005.
Publication Year:
2005
Physical Description:
print, 8 ref 1
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Approximation polynomiale, Polynomial approximation, Aproximación polinomial, Arbre maximal, Spanning tree, Arbol máximo, Méthode minimax, Minimax method, Método minimax, Optimisation combinatoire, Combinatorial optimization, Optimización combinatoria, Plus court chemin, Shortest path, Camino más corto, Problème NP difficile, NP hard problem, Problema NP duro, Problème sac à dos, Knapsack problem, Problema mochila, Programmation dynamique, Dynamic programming, Programación dinámica, Programmation multiobjectif, Multiobjective programming, Programación multiobjetivo, Temps polynomial, Polynomial time, Tiempo polinomial
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
LAMSADE, Université Paris-Dauphine, France
ISSN:
0302-9743
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17246839
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.17246839
Database:
PASCAL Archive

Further Information

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.