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On the Average Case Performance of Some Greedy Approximation Algorithms For the Uncapacitated Facility Location Problem

Published online by Cambridge University Press:  01 September 2007

ABRAHAM D. FLAXMAN ,
ALAN M. FRIEZE  and
JUAN CARLOS VERA
ABRAHAM D. FLAXMAN
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA (e-mail: abie@cmu.edu, alan@random.math.cmu.edu, jvera@andrew.cmu.edu)
ALAN M. FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA (e-mail: abie@cmu.edu, alan@random.math.cmu.edu, jvera@andrew.cmu.edu)
JUAN CARLOS VERA
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA (e-mail: abie@cmu.edu, alan@random.math.cmu.edu, jvera@andrew.cmu.edu)
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Abstract

In combinatorial optimization, a popular approach to NP-hard problems is the design of approximation algorithms. These algorithms typically run in polynomial time and are guaranteed to produce a solution which is within a known multiplicative factor of optimal. Unfortunately, the known factor is often known to be large in pathological instances. Conventional wisdom holds that, in practice, approximation algorithms will produce solutions closer to optimal than their proven guarantees. In this paper, we use the rigorous-analysis-of-heuristics framework to investigate this conventional wisdom.

We analyse the performance of three related approximation algorithms for the uncapacitated facility location problem (from Jain, Mahdian, Markakis, Saberi and Vazirani (2003) and Mahdian, Ye and Zhang (2002)) when each is applied to an instances created by placing n points uniformly at random in the unit square. We find that, with high probability, these 3 algorithms do not find asymptotically optimal solutions, and, also with high probability, a simple plane partitioning heuristic does find an asymptotically optimal solution.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 5 , September 2007 , pp. 713 - 732
Copyright
Copyright © Cambridge University Press 2006

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