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Generalisations Of The Gilmore-Gomory Traveling Salesman Problem And The Gilmore-Gomory Scheme: A Survey

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  • SANTOSH N. KABADI

    (Faculty of Administration, University of New Brunswick, P. O. Box 4400, Fredericton, N.B. E3B 5A3, Canada)

Abstract

One of the first and perhaps the most well-known polynomially solvable special case of the traveling salesman problem (TSP) is the Gilmore-Gomory case (G-G TSP). Gilmore and Gomory presented an interesting patching algorithm for this case with a fairly non-trivial proof of its validity. Their work has motivated a great deal of research in the area leading to various generalisations of their results and thereby identification of fairly large polynomially solvable subclasses of the TSP. These results form a major portion of the literature on solvable cases of the TSP. In this paper, we survey the main results on solvable cases of the TSP which are direct generalisations of the G-G TSP and/or the Gilmore-Gomory patching scheme.

Suggested Citation

  • Santosh N. Kabadi, 2001. "Generalisations Of The Gilmore-Gomory Traveling Salesman Problem And The Gilmore-Gomory Scheme: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 213-235.
    • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:02n03:n:s0219198901000415
    DOI: 10.1142/S0219198901000415
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    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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