TY - JOUR

T1 - Minimizing the sum of the k largest functions in linear time

AU - Ogryczak, Wlodzimierz

AU - Tamir, Arie

PY - 2003/2/14

Y1 - 2003/2/14

N2 - 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].

AB - 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].

KW - Algorithms

KW - Computational geometry

KW - Location

KW - Rectilinear

KW - k-centrum

KW - k-largest

UR - http://www.scopus.com/inward/record.url?scp=0037435797&partnerID=8YFLogxK

U2 - 10.1016/S0020-0190(02)00370-8

DO - 10.1016/S0020-0190(02)00370-8

M3 - מאמר

AN - SCOPUS:0037435797

VL - 85

SP - 117

EP - 122

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 3

ER -