Mathematical Programming

, Volume 131, Issue 1–2, pp 195–220 | Cite as

An improved column generation algorithm for minimum sum-of-squares clustering

Full Length Paper Series A


Given a set of entities associated with points in Euclidean space, minimum sum-of-squares clustering (MSSC) consists in partitioning this set into clusters such that the sum of squared distances from each point to the centroid of its cluster is minimized. A column generation algorithm for MSSC was given by du Merle et al. in SIAM Journal Scientific Computing 21:1485–1505. The bottleneck of that algorithm is the resolution of the auxiliary problem of finding a column with negative reduced cost. We propose a new way to solve this auxiliary problem based on geometric arguments. This greatly improves the efficiency of the whole algorithm and leads to exact solution of instances with over 2,300 entities, i.e., more than 10 times as much as previously done.


Clustering Sum-of-squares Column generation ACCPM 

Mathematics Subject Classification (2000)

65K05 90C27 91C20 


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© Springer and Mathematical Programming Society 2010

Authors and Affiliations

  1. 1.Department of Production EngineeringUniversidade Federal do Rio Grande do NorteRio Grande do NorteBrazil
  2. 2.GERAD and HEC MontréalMontréal, QuébecCanada
  3. 3.LIX, École PolytechniquePalaiseauFrance

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