### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 415-436 |

Number of pages | 22 |

Journal | Journal of Combinatorial Optimization |

Volume | 4 |

Issue number | 4 |

State | Published - 2000 |

### Fingerprint

### 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

*Journal of Combinatorial Optimization*,

*4*(4), 415-436.

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

Research output: Contribution to journal › Article

*Journal of Combinatorial Optimization*, vol. 4, no. 4, pp. 415-436.

}

TY - JOUR

T1 - Generalized Steiner Problems and Other Variants

AU - Dror, Moshe

AU - Haouari, Mohamed

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Complexity

KW - Generalized TSP

KW - NP-hardness

UR - http://www.scopus.com/inward/record.url?scp=0012429694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012429694&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012429694

VL - 4

SP - 415

EP - 436

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 4

ER -