Mathematical Programming

, Volume 93, Issue 1, pp 123–127

A connection between cutting plane theory and the geometry of numbers

  • Gérard Cornuéjols
  • Yanjun Li

DOI: 10.1007/s10107-002-0302-5

Cite this article as:
Cornuéjols, G. & Li, Y. Math. Program. (2002) 93: 123. doi:10.1007/s10107-002-0302-5


In this paper, we relate several questions about cutting planes to a fundamental problem in the geometry of numbers, namely, the closest vector problem. Using this connection we show that the dominance, membership and validity problems are NP-complete for Chvátal and split cuts.

Key words: closest vector problem – dominance problem – membership problem – validity problem – Chvátal cut – split cut – disjunctive cut – Gomory cut 
Mathematics Subject Classification (2000): 90C10 

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gérard Cornuéjols
    • 1
  • Yanjun Li
    • 1
  1. 1.Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, USAUS

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