An 0.828-approximation algorithm for the uncapacitated facility location problem

A.A. Ageev, M.I. Sviridenko
1999 Discrete Applied Mathematics  
The uncapacitated facility location problem in the following formulation is considered: where I and J are ÿnite sets, and bij, ci¿0 are rational numbers. Let Z * denote the optimal value of the problem and let ZR = j∈J mini∈I bij − i∈I ci. Cornuejols et al. (Ann. Discrete Math. 1 (1977) 163-178) prove that for the problem with the additional cardinality constraint |S|6K, a simple greedy algorithm ÿnds a feasible solution S such that (Z(S) − ZR)=(Z * − ZR)¿1 − e −1 ≈ 0:632. We suggest a
more » ... l-time approximation algorithm for the unconstrained version of the problem, based on the idea of randomized rounding due to Goemans and Williamson (SIAM J. Discrete Math. 7 (1994) 656 -666). It is proved that the algorithm delivers a solution S such that (Z(S) − ZR)=(Z * − ZR)¿2( √ 2 − 1) ≈ 0:828. We also show that there exists ¿ 0 such that it is NP-hard to ÿnd an approximate solution S with (Z(S) − ZR)=(Z * − ZR)¿1 − . ? 1999 Elsevier Science B.V. All rights reserved. (A.A.Ageev) 0166-218X/99/$ -see front matter ? 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 -2 1 8 X ( 9 9 ) 0 0 1 0 3 -1
doi:10.1016/s0166-218x(99)00103-1 fatcat:dyvubpflozeczjx2nrc4bflnym