A Linear Bound On The Diameter Of The Transportation Polytope*

We prove that the combinatorial diameter of the skeleton of the polytope of feasible solutions of any m×n transportation problem is at most 8(m+n−2).

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Correspondence to Graham Brightwell.

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* Research for this paper was done while the second and third author were visiting the Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. All authors were supported by the TMR Network DONET of the European Community ERB TMRXCT98-0202.

† Research partially funded by the Dutch BSIK/BRICKS project.

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Brightwell, G., van den Heuvel, J. & Stougie†, L. A Linear Bound On The Diameter Of The Transportation Polytope*. Combinatorica 26, 133–139 (2006). https://doi.org/10.1007/s00493-006-0010-5

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Mathematics Subject Classification (2000):

  • 90C27
  • 90C08