Chordal Editing is Fixed-Parameter Tractable

Authors Yixin Cao, Dániel Marx

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Yixin Cao
Dániel Marx

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Yixin Cao and Dániel Marx. Chordal Editing is Fixed-Parameter Tractable. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 214-225, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


Graph modification problems are typically asked as follows: is there a set of k operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly different versions by allowing different operations. We study a very general graph modification problem which allows all three types of operations: given a graph G and integers k_1, k_2, and k_3, the CHORDAL EDITING problem asks if G can be transformed into a chordal graph by at most k_1 vertex deletions, k_2 edge deletions, and k_3 edge additions. Clearly, this problem generalizes both CHORDAL VERTEX/EDGE DELETION and CHORDAL COMPLETION (also known as MINIMUM FILL-IN). Our main result is an algorithm for CHORDAL EDITING in time 2^O(k.log(k))·n^O(1), where k:=k_1+k_2+k_3; therefore, the problem is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm is both more efficient and conceptually simpler than the previously known algorithm for the special case CHORDAL DELETION.
  • chordal graph
  • parameterized computation
  • graph modification problems
  • chordal deletion
  • chordal completion
  • clique tree decomposition
  • holes
  • simplic


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