Separating clique tree and bipartition inequalities in polynomial time

  • Robert D. Carr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 920)


Many important cutting planes have been discovered for the traveling salesman problem. Among them are the clique tree inequalities and the more general bipartition inequalities. Little is known in the way of exact algorithms for separating these inequalities in polynomial time in the size of the fractional point X* which is being separated. An algorithm is presented here that separates bipartition inequalities of a fixed number of handles and teeth, which includes clique tree inequalities of a fixed number of handles and teeth, in polynomial time.


Polynomial Time Travel Salesman Problem Valid Inequality Intersection Graph Linear Programming Relaxation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. C. Boyd and W. H. Cunningham (1991), Small travelling salesman polytopes, Mathematics of Operations Research 16, 259–271Google Scholar
  2. 2.
    M. Grotschel and W. R. Pulleyblank (1986), Clique tree inequalities and the symmetric traveling salesman problem, Mathematics of Operations Research 11, 537–569Google Scholar
  3. 3.
    M. Junger, G. Reinelt, and G. Rinaldi (1994), The traveling salesman problem, Istituto Di Analisi Dei Sistemi Ed Informatica, R. 375, p. 64Google Scholar
  4. 4.
    M. W. Padberg and M.R. Rao (1982), Odd minimum cut sets and b-matchings, Math. Oper. Res. 7, 67–80Google Scholar
  5. 5.
    M. Padberg and G. Rinaldi (1990), Facet identification for the symmetric traveling salesman polytope, Mathematical Programming 47 219–257Google Scholar
  6. 6.
    D. Naddef (1992), The binested inequalities for the symmetric traveling salesman polytope, Mathematics of Operations Research, Vol. 17, No. 4, Nov.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Robert D. Carr
    • 1
  1. 1.Department of MathematicsCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations