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A Golden Ratio Parameterized Algorithm for Cluster Editing

  • Sebastian Böcker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)

Abstract

The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known. We present a novel search tree algorithm for the problem, which improves running time from O*(1.76 k ) to O*(1.62 k ). In detail, we can show that we can always branch with branching vector (2,1) or better, resulting in the golden ratio as the base of the search tree size. Our algorithm uses a well-known transformation to the integer-weighted counterpart of the problem. To achieve our result, we combine three techniques: First, we show that zero-edges in the graph enforce structural features that allow us to branch more efficiently. Second, by repeatedly branching we can isolate vertices, releasing costs. Finally, we use a known characterization of graphs with few conflicts.

Keywords

Search Tree Input Graph Parity Property Golden Ratio Polynomial Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sebastian Böcker
    • 1
  1. 1.Lehrstuhl für BioinformatikFriedrich-Schiller-Universität JenaJenaGermany

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