### Divide-and-conquer approximation algorithms via spreading metricsDivide-and-conquer approximation algorithms via spreading metrics

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 Author Even, Guy ♦ Naor, Joseph Seffi ♦ Rao, Satish ♦ Schieber, Baruch Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2000 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Approximation algorithms ♦ Divide and conquer ♦ Feedback set ♦ Linear arrangement ♦ Multicut ♦ Spreading metrics Abstract We present a novel divide-and-conquer paradigm for approximating NP-hard graph optimization problems. The paradigm models graph optimization problems that satisfy two properties: First, a divide-and-conquer approach is applicable. Second, a fractional spreading metric is computable in polynomial time. The spreading metric assigns lengths to either edges or vertices of the input graph, such that all subgraphs for which the optimization problem is nontrivial have large diameters. In addition, the spreading metric provides a lower bound, t , log $\textit{k}$ log log $\textit{k}})$ where $\textit{k}$ denotes the number of “interesting” vertices in the problem instance, and is at most the number of vertices. We present seven problems that can be formulated to fit the paradigm. For all these problems our algorithm improves previous results. The problems are: (1) linear arrangement; (2) embedding a graph in a $\textit{d}-dimensional$ mesh; (3) interval graph completion; (4) minimizing storage-time product; (5) subset feedback sets in directed graphs and multicuts in circular networks; (6) symmetric multicuts in directed networks; (7) balanced partitions and $\textit{p}-separators$ (for small values of $\textit{p})$ in directed graphs. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2000-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 47 Issue Number 4 Page Count 32 Starting Page 585 Ending Page 616

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Source: ACM Digital Library