Fritz, A, Hellmuth, M orcid.org/0000-0002-1620-5508, Stadler, PF et al. (1 more author) (2020) Cograph editing: Merging modules is equivalent to editing P_4s. Art of Discrete and Applied Mathematics, 3 (2). #P2.01. ISSN 2590-9770
Abstract
The modular decomposition of a graph G = (V, E) does not contain prime modules if and only if G is a cograph, that is, if no quadruple of vertices induces a simple connected path P4. The cograph editing problem consists in inserting into and deleting from G a set F of edges so that H = (V, E △ F) is a cograph and |F| is minimum. This NP-hard combinatorial optimization problem has recently found applications, e.g., in the context of phylogenetics. Efficient heuristics are hence of practical importance. The simple characterization of cographs in terms of their modular decomposition suggests that instead of editing G one could operate directly on the modular decomposition. We show here that editing the induced P4s is equivalent to resolving prime modules by means of a suitable defined merge operation on the submodules. Moreover, we characterize so-called module-preserving edit sets and demonstrate that optimal pairwise sequences of module-preserving edit sets exist for every non-cograph. This eventually leads to an exact algorithm for the cograph editing problem as well as fixed-parameter tractable (FPT) results when cograph editing is parameterized by the so-called modular-width. In addition, we provide two heuristics with time complexity O(|V|3), resp., O(|V|2).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Cograph editing, modular decomposition, module merge, prime modules, P 4 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 May 2020 13:13 |
Last Modified: | 06 May 2020 13:13 |
Status: | Published |
Publisher: | University of Primorska Press |
Identification Number: | 10.26493/2590-9770.1252.e71 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:160328 |