A systematic approach to bound factor-revealing LPs and its application to the metric and squared metric facility location problems

• 成果类型: Article
• 署名作者: Fernandes, Cristina G.; Meira, Luis A. A.; Miyazawa, Flavio K.; Pedrosa, Lehilton L. C.
• 署名单位: Universidade de Sao Paulo; Universidade Estadual de Campinas; Universidade Estadual de Campinas
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0821-x
• 发表日期: 2015
• 页码: 655-685
• 关键词: approximation algorithms

摘要

A systematic technique to bound factor-revealing linear programs is presented. We show how to derive a family of upper bound factor-revealing programs (UPFRP), and show that each such program can be solved by a computer to bound the approximation factor of an associated algorithm. Obtaining an UPFRP is straightforward, and can be used as an alternative to analytical proofs, that are usually very long and tedious. We apply this technique to the metric facility location problem (MFLP) and to a generalization where the distance function is a squared metric. We call this generalization the squared metric facility location problem (SMFLP), and prove that there is no approximation factor better than 2.04, assuming P not equal NP. Then, we analyze the best known algorithms for the MFLP based on primal-dual and LP-rounding techniques when they are applied to the SMFLP. We prove very tight bounds for these algorithms, and show that the LP-rounding algorithm achieves a ratio of 2.04, and therefore has the best possible factor for the SMFLP. We use UPFRPs in the dualfitting analysis of the primal-dual algorithms for both the SMFLP and the MFLP, improving some of the previous analysis for the MFLP.