Cograph Editing: Merging Modules is equivalent to Editing P4's Article Swipe
Marc Hellmuth
,
Adrian Fritz
,
Nicolas Wieseke
,
Peter F. Stadler
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1702.07499
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1702.07499
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 $P_4$. The cograph editing problem consists in inserting into and deleting from $G$ a set $F$ of edges so that $H=(V,EΔF)$ 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 $P_4$s 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., $O(|V|^2)$.
Related Topics
Concepts
Heuristics
Cograph
Computer science
Combinatorics
Modular design
Path (computing)
Graph
Modular decomposition
Theoretical computer science
Mathematics
Pathwidth
Programming language
Line graph
Operating system
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1702.07499
- https://arxiv.org/pdf/1702.07499
- OA Status
- green
- References
- 44
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2785197145
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https://openalex.org/W2785197145Canonical identifier for this work in OpenAlex
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Cograph Editing: Merging Modules is equivalent to Editing P4'sWork title
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preprintOpenAlex work type
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enPrimary language
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2017Year of publication
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2017-02-24Full publication date if available
- Authors
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Marc Hellmuth, Adrian Fritz, Nicolas Wieseke, Peter F. StadlerList of authors in order
- Landing page
-
https://arxiv.org/abs/1702.07499Publisher landing page
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https://arxiv.org/pdf/1702.07499Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1702.07499Direct OA link when available
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| abstract_inverted_index.no | 23 |
| abstract_inverted_index.of | 3, 25, 48, 73, 79, 85, 89, 96, 123, 145 |
| abstract_inverted_index.on | 103, 129 |
| abstract_inverted_index.so | 50 |
| abstract_inverted_index.to | 117, 156 |
| abstract_inverted_index.we | 133, 183 |
| abstract_inverted_index.$F$ | 47 |
| abstract_inverted_index.$G$ | 16, 44, 98 |
| abstract_inverted_index.The | 0, 33, 82 |
| abstract_inverted_index.and | 13, 41, 56, 139 |
| abstract_inverted_index.are | 77 |
| abstract_inverted_index.for | 150, 160 |
| abstract_inverted_index.has | 65 |
| abstract_inverted_index.is, | 21 |
| abstract_inverted_index.not | 8 |
| abstract_inverted_index.one | 99 |
| abstract_inverted_index.set | 46 |
| abstract_inverted_index.the | 71, 104, 112, 130, 161, 178 |
| abstract_inverted_index.two | 185 |
| abstract_inverted_index.This | 60, 153 |
| abstract_inverted_index.does | 7 |
| abstract_inverted_index.edit | 137, 147 |
| abstract_inverted_index.from | 43 |
| abstract_inverted_index.here | 109 |
| abstract_inverted_index.into | 40 |
| abstract_inverted_index.only | 14 |
| abstract_inverted_index.path | 31 |
| abstract_inverted_index.sets | 138, 148 |
| abstract_inverted_index.show | 108 |
| abstract_inverted_index.that | 20, 51, 94, 110, 141 |
| abstract_inverted_index.time | 188 |
| abstract_inverted_index.well | 166 |
| abstract_inverted_index.when | 172 |
| abstract_inverted_index.with | 187 |
| abstract_inverted_index.$|F|$ | 57 |
| abstract_inverted_index.(FPT) | 170 |
| abstract_inverted_index.could | 100 |
| abstract_inverted_index.e.g., | 69 |
| abstract_inverted_index.edges | 49 |
| abstract_inverted_index.every | 151 |
| abstract_inverted_index.exact | 158 |
| abstract_inverted_index.exist | 149 |
| abstract_inverted_index.found | 67 |
| abstract_inverted_index.graph | 5 |
| abstract_inverted_index.hence | 78 |
| abstract_inverted_index.leads | 155 |
| abstract_inverted_index.means | 122 |
| abstract_inverted_index.merge | 127 |
| abstract_inverted_index.prime | 10, 119 |
| abstract_inverted_index.terms | 88 |
| abstract_inverted_index.their | 90 |
| abstract_inverted_index.$P_4$. | 32 |
| abstract_inverted_index.$P_4$s | 114 |
| abstract_inverted_index.resp., | 191 |
| abstract_inverted_index.simple | 29, 83 |
| abstract_inverted_index.NP-hard | 61 |
| abstract_inverted_index.cograph | 34, 55, 162, 173 |
| abstract_inverted_index.contain | 9 |
| abstract_inverted_index.context | 72 |
| abstract_inverted_index.defined | 126 |
| abstract_inverted_index.editing | 35, 97, 111, 163, 174 |
| abstract_inverted_index.induced | 113 |
| abstract_inverted_index.induces | 27 |
| abstract_inverted_index.instead | 95 |
| abstract_inverted_index.modular | 1, 91, 105 |
| abstract_inverted_index.modules | 11, 120 |
| abstract_inverted_index.operate | 101 |
| abstract_inverted_index.optimal | 142 |
| abstract_inverted_index.problem | 36, 64, 164 |
| abstract_inverted_index.provide | 184 |
| abstract_inverted_index.results | 171 |
| abstract_inverted_index.cograph, | 19 |
| abstract_inverted_index.cographs | 86 |
| abstract_inverted_index.consists | 37 |
| abstract_inverted_index.deleting | 42 |
| abstract_inverted_index.directly | 102 |
| abstract_inverted_index.minimum. | 59 |
| abstract_inverted_index.pairwise | 143 |
| abstract_inverted_index.recently | 66 |
| abstract_inverted_index.suggests | 93 |
| abstract_inverted_index.suitable | 125 |
| abstract_inverted_index.vertices | 26 |
| abstract_inverted_index.$G=(V,E)$ | 6 |
| abstract_inverted_index.Efficient | 75 |
| abstract_inverted_index.Moreover, | 132 |
| abstract_inverted_index.addition, | 182 |
| abstract_inverted_index.algorithm | 159 |
| abstract_inverted_index.connected | 30 |
| abstract_inverted_index.inserting | 39 |
| abstract_inverted_index.operation | 128 |
| abstract_inverted_index.practical | 80 |
| abstract_inverted_index.quadruple | 24 |
| abstract_inverted_index.resolving | 118 |
| abstract_inverted_index.sequences | 144 |
| abstract_inverted_index.so-called | 135, 179 |
| abstract_inverted_index.tractable | 169 |
| abstract_inverted_index.complexity | 189 |
| abstract_inverted_index.equivalent | 116 |
| abstract_inverted_index.eventually | 154 |
| abstract_inverted_index.heuristics | 76, 186 |
| abstract_inverted_index.$O(|V|^2)$. | 192 |
| abstract_inverted_index.$O(|V|^3)$, | 190 |
| abstract_inverted_index.demonstrate | 140 |
| abstract_inverted_index.importance. | 81 |
| abstract_inverted_index.submodules. | 131 |
| abstract_inverted_index.$H=(V,EΔF)$ | 52 |
| abstract_inverted_index.characterize | 134 |
| abstract_inverted_index.non-cograph. | 152 |
| abstract_inverted_index.optimization | 63 |
| abstract_inverted_index.applications, | 68 |
| abstract_inverted_index.combinatorial | 62 |
| abstract_inverted_index.decomposition | 2, 92 |
| abstract_inverted_index.parameterized | 176 |
| abstract_inverted_index.decomposition. | 106 |
| abstract_inverted_index.modular-width. | 180 |
| abstract_inverted_index.phylogenetics. | 74 |
| abstract_inverted_index.fixed-parameter | 168 |
| abstract_inverted_index.characterization | 84 |
| abstract_inverted_index.module-preserving | 136, 146 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |