### Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004

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 Author Bar-Yehuda, Reuven ♦ Bendel, Keren ♦ Freund, Ari ♦ Rawitz, Dror Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2004 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Approximation algorithms ♦ Fractional local ratio ♦ Local ratio technique Abstract The local ratio technique is a methodology for the design and analysis of algorithms for a broad range of optimization problems. The technique is remarkably simple and elegant, and yet can be applied to several classical and fundamental problems (including covering problems, packing problems, and scheduling problems). The local ratio technique uses elementary math and requires combinatorial insight into the structure and properties of the problem at hand. Typically, when using the technique, one has to invent a weight function for a problem instance under which every "reasonable" solution is "good." The local ratio technique is closely related to the $\textit{primal-dual}$ schema, though it is not based on weak LP duality (which is the basis of the primal-dual approach) since it is not based on linear programming.In this survey we, introduce the local ratio technique and demonstrate its use in the design and analysis of algorithms for various problems. We trace the evolution path of the technique since its inception in the 1980's, culminating with the most recent development, namely, fractional local ratio, which can be viewed as a new LP rounding technique. ISSN 03600300 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2004-12-01 Publisher Place New York e-ISSN 15577341 Journal ACM Computing Surveys (CSUR) Volume Number 36 Issue Number 4 Page Count 42 Starting Page 422 Ending Page 463

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Source: ACM Digital Library