A Hard Problem: The TSP

  • Dieter Jungnickel
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 5)

Abstract

In this book, we have concentrated on those optimization problems which allow efficient (that is, polynomial time) algorithms. In contrast, the final chapter deals with an archetypical NP-complete problem: the travelling salesman problem already introduced in Chap.  1. It is one of the most famous and important problems in all of combinatorial optimization—with manyfold applications in such diverse areas as logistics, genetics, telecommunications, and neuroscience—and has been the subject of extensive study for about 60 years. We saw in Chap.  2 that no efficient algorithms are known for NP-complete problems, and that it is actually quite likely that no such algorithms can exist. Now we address the question of how such hard problems—which regularly occur in practical applications—might be approached: one uses, for instance, approximation techniques, heuristics, relaxations, post-optimization, local search, and complete enumeration. We shall explain these methods only for the TSP, but they are typical for dealing with hard problems in general. We will also brie y explain the idea of a further extremely important approach—via polyhedra—to solving hard problems and present a list of notable large scale TSPs which were solved to optimality.

Keywords

Minimal Span Tree Travel Salesman Problem Large Instance Local Search Algorithm Hamiltonian Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dieter Jungnickel
    • 1
  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany

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