Chordal Editing is Fixed-Parameter Tractable

Graph modification problems typically ask for a small set of 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...

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Bibliographic Details
Published in:Algorithmica Vol. 75; no. 1; pp. 118 - 137
Main Authors: Cao, Yixin, Marx, Dániel
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2016
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Theory of Computation
Chordal deletion
Parameterized computation
Clique tree decomposition
Chordal completion
Chordal graph
Graph modification problems
Holes
Simplicial vertex sets
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:Graph modification problems typically ask for a small set of 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 that allows all three types of operations: given a graph and integers , and , the chordal editing problem asks whether can be transformed into a chordal graph by at most vertex deletions, edge deletions, and edge additions. Clearly, this problem generalizes both chordal deletion and chordal completion (also known as minimum fill - in ). Our main result is an algorithm for chordal editing in time , where and is the number of vertices of . 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 .
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-015-0014-x