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Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs

Authors Philip N. Klein, Claire Mathieu, Hang Zhou

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Philip N. Klein
Claire Mathieu
Hang Zhou

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Philip N. Klein, Claire Mathieu, and Hang Zhou. Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 554-567, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.STACS.2015.554

Abstract

In correlation clustering, the input is a graph with edge-weights, where every edge  is labelled either + or - according to similarity of its endpoints. The goal is to produce a partition of the vertices that disagrees with the edge labels as little as possible.

In two-edge-connected augmentation, the input is a graph with edge-weights and a subset R of edges of the graph. The goal is to produce a minimum weight subset S of edges of the graph, such that for every edge in R, its endpoints are two-edge-connected in R\cup S.

For planar graphs, we prove that correlation clustering reduces to two-edge-connected augmentation, and that both problems have a polynomial-time approximation scheme.

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Keywords
  • correlation clustering
  • two-edge-connected augmentation
  • polynomial-time approximation scheme
  • planar graphs

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