On the mixed Chinese postman problem

https://doi.org/10.1016/0167-6377(93)90021-8Get rights and content

Abstract

The mixed Chinese postman problem is a version of the well-known Chinese postman problem in which the underlying graph consists of both directed and undirected edges. We give an integer linear programming formulation for this problem and then show that the extreme points of its linear relaxation polyhedron are all half-integral.

References (9)

  • J. Edmonds

    The Chinese postman's problem

    Oper. Res.

    (1965)
  • J. Edmonds et al.

    Matching, Euler tours and the Chinese postman

    Math. Programming

    (1973)
  • L.R. Ford et al.

    Flows in Networks

    (1962)
  • G.N. Frederickson

    Approximation algorithms for some postman problems

    J. ACM

    (1979)
There are more references available in the full text version of this article.

Cited by (14)

  • Approximation algorithms for solving the constrained arc routing problem in mixed graphs

    2014, European Journal of Operational Research
    Citation Excerpt :

    Comprehensive surveys, latest advances and new challenges on the MCPP are available in Dror (2000), Golden et al. (2008) and Toth and Vigo (2002). Integer and linear programming formulations of the postman problems have generated great interest in recent years (Nobert & Picard, 1996; Ralphs, 1993). Ralphs (1993) showed that a linear relaxation of the MCPP has optimal solutions that are half-integral.

  • A comparison of two different formulations for arc routing problems on mixed graphs

    2006, Computers and Operations Research
    Citation Excerpt :

    As the formulation proposed by Nobert and Picard [6] for the MCPP, it is based on the characterization of an Eulerian mixed graph given by Ford and Fulkerson [3]. But some routing problems on mixed graphs have also been modelled using two variables associated to the same edge (see Kappauf and Koehler [9], Christofides et al. [4], Grötschel and Win [5] and Ralphs [10]), each variable representing its traversal in the corresponding direction. In fact, during the revision of [7], an anonymous referee argued that formulating the MGRP using two variables for each edge would produce a stronger LP relaxation.

  • Chapter 5 Arc routing methods and applications

    1995, Handbooks in Operations Research and Management Science
  • A 3/2-Approximation algorithm for the mixed postman problem

    1999, SIAM Journal on Discrete Mathematics
View all citing articles on Scopus

Research partially supported by an NSF PYI award CCR-89-96272 with matching support from UPS, and Sun Microsystems, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.

View full text