Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Traveling Salesman Problem

  • Karla L. Hoffman
  • Manfred Padberg
  • Giovanni Rinaldi
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_1068

Introduction

The traveling salesman problem (TSP) has commanded much attention from mathematicians and computer scientists specifically because it is so easy to describe and so difficult to solve. The problem can simply be stated as: if a traveling salesman wishes to visit exactly once each of a list of m cities (where the cost of traveling from city i to city j is cij) and then return to the home city, what is the least costly route the traveling salesman can take? A complete historical development of this and related problems can be found in Hoffman and Wolfe (1985), Applegate et al. (2006), and Cook (2011).

The importance of the TSP is that it is representative of a larger class of problems known as combinatorial optimization problems. The TSP problem belongs in the class of such problems known as NP-complete. Specifically, if one can find an efficient (i.e., polynomial-time) algorithm for the traveling salesman problem, then efficient algorithms could be found for all other...

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Karla L. Hoffman
    • 1
  • Manfred Padberg
    • 2
  • Giovanni Rinaldi
    • 3
  1. 1.George Mason UniversityFairfaxUSA
  2. 2.New York UniversityNew YorkUSA
  3. 3.CNR – Istituto di Analisi dei Sistemi ed Informatica (IASI)RomeItaly