Generalized Steiner Problems and Other Variants

Moshe Dror and Mohamed Haouari
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Moshe Dror: The University of Arizona
Mohamed Haouari: Ecole Polytechnique de Tunisie

Journal of Combinatorial Optimization, 2000, vol. 4, issue 4, No 2, 415-436

Abstract: Abstract In this paper, we examine combinatorial optimization problems by considering the case where the set N (the ground set of elements) is expressed as a union of a finite number of m nonempty distinct subsets N 1,...,N m. The term we use is the generalized Steiner problems coined after the Generalized Traveling Salesman Problem. We have collected a short list of classical combinatorial optimization problems and we have recast each of these problems in this broader framework in an attempt to identify a linkage between these “generalized” problems. In the literature one finds generalized problems such as the Generalized Minimum Spanning Tree (GMST), Generalized Traveling Salesman Problem (GTSP) and Subset Bin-packing (SBP). Casting these problems into the new problem setting has important implications in terms of the time effort required to compute an optimal solution or a “good” solution to a problem. We examine questions like “is the GTSP “harder” than the TSP?” for a number of paradigmatic problems starting with “easy” problems such as the Minimal Spanning Tree, Assignment Problem, Chinese Postman, Two-machine Flow Shop, and followed by “hard” problems such as the Bin-packing, and the TSP.

Keywords: complexity; NP-hardness; generalized TSP; approximation algorithms (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (10)

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DOI: 10.1023/A:1009881326671

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