Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey

The traveling salesman problem (TSP) belongs to the most basic, most important, and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently in polynomial time. We survey these special cases with emphasis on the...

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Bibliographic Details
Published in:SIAM review 1998-09, Vol.40 (3), p.496-546
Main Authors: Burkard, Rainer E., Deῐneko, Vladimir G., van Dal, René, Jack A. A. van der Veen, Woeginger, Gerhard J.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Exact sciences and technology
Graph theory
Heuristics
Itinerant sales
Mathematical models
Mathematical programming
Mathematics
Matrices
Operational research and scientific management
Operational research. Management science
Polynomials
Rectangles
Sciences and techniques of general use
Theoretical computing
Traveling salesman problem
Vanes
Vertices
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Summary:The traveling salesman problem (TSP) belongs to the most basic, most important, and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently in polynomial time. We survey these special cases with emphasis on the results that have been obtained during the decade 1985-1995. This survey complements an earlier survey from 1985 compiled by Gilmore, Lawler, and Shmoys [The Traveling Salesman Problem-A Guided Tour of Combinatorial Optimization, Wiley, Chichester, pp. 87-143].
ISSN:0036-1445
1095-7200
DOI:10.1137/S0036144596297514