Minimizing the sum of the k largest functions in linear time

Wlodzimierz Ogryczak, Arie Tamir

Research output: Contribution to journalArticlepeer-review

Abstract

Given a collection of n functions defined on ℝd, and a polyhedral set Q ⊂ ℝd, we consider the problem of minimizing the sum of the k largest functions of the collection over Q. Specifically we focus on collections of linear functions and several classes of convex, piecewise linear functions which are defined by location models. We present simple linear programming formulations for these optimization models which give rise to linear time algorithms when the dimension d is fixed. Our results improve complexity bounds of several problems reported recently by Tamir [Discrete Appl. Math. 109 (2001) 293-307], Tokuyama [Proc. 33rd Annual ACM Symp. on Theory of Computing, 2001, pp. 75-84] and Kalcsics, Nickel, Puerto and Tamir [Oper. Res. Lett. 31 (1984) 114-127].

Original languageEnglish
Pages (from-to)117-122
Number of pages6
JournalInformation Processing Letters
Volume85
Issue number3
DOIs
StatePublished - 14 Feb 2003

Keywords

  • Algorithms
  • Computational geometry
  • Location
  • Rectilinear
  • k-centrum
  • k-largest

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