Generalized Steiner Problems and Other Variants

Moshe Dror, Mohamed Haouari

Research output: Contribution to journalArticle

22 Scopus citations

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
DOIs
StatePublished - Jan 1 2000

Keywords

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

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Generalized Steiner Problems and Other Variants'. Together they form a unique fingerprint.

  • Cite this