Mathematical Programming

, Volume 128, Issue 1–2, pp 171–203

A large class of facets for the K-median polytope

Full Length Paper Series A

DOI: 10.1007/s10107-009-0301-x

Cite this article as:
Zhao, W. & Posner, M.E. Math. Program. (2011) 128: 171. doi:10.1007/s10107-009-0301-x


The polyhedral structure of the K-median problem is examined. We present an extended formulation that is integral but grows exponentially with the number of nodes. Then, some extra variables are projected out. Based on the reduced formulation, we develop two basic properties for facets of K-median problem. By applying the two properties, we generalize two known classes of facets, de Vries facets and de Farias facets. The computational study illustrates that the generalization is significant.


Facets Polyhedral description 

Mathematics Subject Classification (2000)

90C10 Integer programming 90C27 Combinatorial optimization 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut 90C35 Programming involving graphs or networks [See also 90C27] 90C09 Boolean programming 

Copyright information

© Springer and Mathematical Programming Society 2009

Authors and Affiliations

  1. 1.Olin Business SchoolWashington University in St. LouisSt. LouisUSA
  2. 2.Department of Integrated Systems EngineeringThe Ohio State UniversityColumbusUSA

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