Paper Info
Title
Improved Approximation Algorithm for k-level Uncapacitated Facility Location Problem (with Penalties)
Abstract
AbstractWe study the k-level uncapacitated facility location problem (k-level UFL) in which clients need to be connected with paths crossing open facilities of k types (levels). In this paper we first propose an approximation algorithm that for any constant k, in polynomial time, delivers solutions of cost at most k times OPT, where k is an increasing function of k, with limk k=3$\lim _{k\to \infty } \alpha _{k} = 3$. Our algorithm rounds a fractional solution to an extended LP formulation of the problem. The rounding builds upon the technique of iteratively rounding fractional solutions on trees (Garg, Konjevod, and Ravi SODA'98) originally used for the group Steiner tree problem. We improve the approximation ratio for k-level UFL for all k 3, in particular we obtain the ratio equal 2.02, 2.14, and 2.24 for k = 3,4, and 5.Second, we give a simple interpretation of the randomization process (Li ICALP'2011) for 1-level UFL in terms of solving an auxiliary (factor revealing) LP. Armed with this simple view point, we exercise the randomization on our algorithm for the k-level UFL. We further improve the approximation ratio for all k 3, obtaining 1.97, 2.09, and 2.19 for k = 3,4, and 5.Third, we extend our algorithm to the k-level UFL with penalties (k-level UFLWP), in which the setting is the same as k-level UFL except that the planner has the option to pay a penalty instead of connecting chosen clients.
Year
DOI
Venue
2016
10.1007/s00224-014-9575-3
Periodicals
Keywords
Field
DocType
Facility location,Approximation algorithms
Approximation algorithm,Discrete mathematics,Combinatorics,Steiner tree problem,Facility location problem,Rounding,Time complexity,Mathematics
Journal
Volume
Issue
ISSN
58
1
1432-4350
Citations 
PageRank 
References 
3
0.38
19
Authors
3
Name
Order
Citations
PageRank
Jaroslaw Byrka152331.45
Shanfei Li251.45
Bartosz Rybicki3434.80