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 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0037435797
SN - 0020-0190
VL - 85
SP - 117
EP - 122
JO - Information Processing Letters
JF - Information Processing Letters
IS - 3
ER -