Complexity and parameterized algorithms for Cograph Editing
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TL;DR: This paper first shows that this problem is NP-hard by a reduction from Exact 3-Cover, and presents a parameterized algorithm based on a refined search tree technique with a running time of O(4.612^k+|V|^4^.^5), which improves the trivial algorithm of running time O(6^k+.
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About: This article is published in Theoretical Computer Science. The article was published on 01 Nov 2012. and is currently open access. The article focuses on the topics: Cograph & Computational complexity theory.
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Citations
Phylogenomics with paralogs
Marc Hellmuth,Nicolas Wieseke,Marcus Lechner,Hans-Peter Lenhof,Martin Middendorf,Peter F. Stadler +5 more
TL;DR: It is demonstrated that the distribution of paralogs in large gene families contains in itself sufficient phylogenetic signal to infer fully resolved species phylogenies, and genome-wide data sets are sufficient to generate fully resolved phylogenetic trees, even in the presence of horizontal gene transfer.
129
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A Polynomial Kernel for Trivially Perfect Editing
TL;DR: This work gives a kernel with \(O(k^7)\) vertices for Trivially Perfect Editing, the problem of adding or removing at most k edges in order to make a given graph trivially perfect, and proves that it cannot be solved in time unless the exponential time hypothesis fails.
40
Best match graphs and reconciliation of gene trees with species trees
Manuela Geiß,Marcos González Laffitte,Alitzel López Sánchez,Dulce I. Valdivia,Dulce I. Valdivia,Marc Hellmuth,Marc Hellmuth,Maribel Hernández Rosales,Peter F. Stadler +8 more
TL;DR: In this article, the orthology graph is shown to be a subgraph of the reciprocal best match graph (RBMG), and conditions under which an RBMG that is a cograph identifies the correct orthlogy relation.
On tree representations of relations and graphs: symbolic ultrametrics and cograph edge decompositions
TL;DR: In this paper, the problem of finding the optimal cograph edge k-decomposition for a given edge-colored undirected graph G is studied and the complexity of the problem is shown to be NP-hard.
32
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On the Threshold of Intractability
TL;DR: In this article, it was shown that the problem of threshold editing is NP-complete, and a subexponential time parameterized algorithm was proposed to solve it in O(surd k \log k) + poly(n) time.
References
A linear recognition algorithm for cographs
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Modular decomposition and transitive orientation
TL;DR: This work gives O(n+m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph and linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparable graphs and their complements.
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Fixed-parameter tractability of graph modification problems for hereditary properties
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A tree representation for P 4 -sparse graphs
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TL;DR: This work gives several characterizations for P4-sparse graphs and shows that they can be constructed from single-vertex graphs by a finite sequence of operations and implies that they admit a tree representation unique up to isomorphism.
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Automated Generation of Search Tree Algorithms for Hard Graph Modification Problems
TL;DR: A framework for an automated generation of exact search tree algorithms for NP-hard problems, based on complicated case distinctions, which may lead to a much simpler process of developing and analyzing these algorithms and improve upper bounds on search tree sizes.
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