Tight integral duality gap in the Chinese Postman problem

Ephraim Korach, Michal Penn

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Let G = (V, E) be a graph and let w be a weight function w:E →Z+. Let {Mathematical expression} be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutions to the Chinese Postman problem). The main theorem of this paper gives a tight upper bound on the difference between the minimum weight T-join and the maximum weight integral packing of T-cuts. This difference is called the (T-join) integral duality gap. Let τw be the minimum weight of a T-join, and let vw be the maximum weight of an integral packing of T-cuts. If F is a non-empty minimum weight T-join, and nF is the number of components of F, then we prove that τw-vw≤nF-1. This result unifies and generalizes Fulkerson's result for |T|=2 and Seymour's result for |T|= 4. For a certain integral multicommodity flow problem in the plane, which was recently proved to be NP-complete, the above result gives a solution such that for every commodity the flow is less than the demand by at most one unit.

Original languageEnglish
Pages (from-to)183-191
Number of pages9
JournalMathematical Programming
Issue number1-3
StatePublished - 1 Apr 1992
Externally publishedYes


  • Chinese Postman problem
  • T-cuts
  • integral LP duality
  • integral packing
  • plane integral multicommodity flows

ASJC Scopus subject areas

  • Software
  • General Mathematics


Dive into the research topics of 'Tight integral duality gap in the Chinese Postman problem'. Together they form a unique fingerprint.

Cite this