Generalized Steiner Problems and Other Variants

Moshe Dror, Mohamed Haouari

Research output: Contribution to journalArticle

21 Citations (Scopus)

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 N1, . . . , Nm. 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.

Original languageEnglish (US)
Pages (from-to)415-436
Number of pages22
JournalJournal of Combinatorial Optimization
Volume4
Issue number4
StatePublished - 2000

Fingerprint

Steiner's problem
Traveling salesman problem
Combinatorial optimization
Bins
Travelling salesman problems
Set theory
Bin Packing
Casting
Combinatorial Optimization Problem
Minimal Spanning Tree
Subset
Flow Shop
Minimum Spanning Tree
Assignment Problem
Linkage
Union
Optimal Solution
Distinct

Keywords

  • Approximation algorithms
  • Complexity
  • Generalized TSP
  • NP-hardness

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Generalized Steiner Problems and Other Variants. / Dror, Moshe; Haouari, Mohamed.

In: Journal of Combinatorial Optimization, Vol. 4, No. 4, 2000, p. 415-436.

Research output: Contribution to journalArticle

Dror, Moshe ; Haouari, Mohamed. / Generalized Steiner Problems and Other Variants. In: Journal of Combinatorial Optimization. 2000 ; Vol. 4, No. 4. pp. 415-436.
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