Journal ArticleDOI
Fixed-parameter tractability of graph modification problems for hereditary properties
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The problem of deciding whether a graph can be made into a chordal graph by adding a fixed number k of edges is shown to be solvable in 0( 4’( k + 1) --3’2 (m + n) ) time, and is thus fixed-parameter tractable.About:
This article is published in Information Processing Letters.The article was published on 1996-05-27. It has received 431 citations till now. The article focuses on the topics: Complement graph & Strength of a graph.read more
Citations
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Invitation to fixed-parameter algorithms
TL;DR: This paper discusses Fixed-Parameter Algorithms, Parameterized Complexity Theory, and Selected Case Studies, and some of the techniques used in this work.
Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Journal ArticleDOI
Minimal triangulations of graphs: A survey
TL;DR: This survey presents and ties together a variety of algorithms for computing minimal triangulations of both general and restricted graph classes in a unified modern notation, keeping an emphasis on the algorithms.
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Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal, and Proper Interval Graphs
TL;DR: The parameterized complexity of three NP-hard graph completion problems, motivated by molecular biology, is studied and it is shown that the parameterized version of the strongly chordal graph completion problem is FPT by giving an O(ck m log n)-time algorithm for it.
Journal ArticleDOI
Complexity Classification of Some Edge Modification Problems
TL;DR: This paper proves the NP-hardness of a variety of edge modification problems with respect to some well-studied classes of graphs, including perfect, chordal, chain, comparability, split and asteroidal triple free.
References
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Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Journal ArticleDOI
Algorithmic Aspects of Vertex Elimination on Graphs
TL;DR: A graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations is considered, and it is conjecture that the problem of finding a minimum ordering is NP-complete.