3 Search Results for "Hellmuth, Marc"

Document
DOI: 10.4230/LIPIcs.WADS.2025.36
On the Complexity of Minimising the Moving Distance for Dispersing Objects

Authors: Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an O(n log n)-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the L₁ and L₂ distances.
Cite as

Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. On the Complexity of Minimising the Moving Distance for Dispersing Objects. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{honoratodroguett_et_al:LIPIcs.WADS.2025.36,
  author =	{Honorato-Droguett, Nicol\'{a}s and Kurita, Kazuhiro and Hanaka, Tesshu and Ono, Hirotaka},
  title =	{{On the Complexity of Minimising the Moving Distance for Dispersing Objects}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.36},
  URN =		{urn:nbn:de:0030-drops-242673},
  doi =		{10.4230/LIPIcs.WADS.2025.36},
  annote =	{Keywords: Intersection graphs, Optimisation, Graph modification}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.64
Cluster Editing on Cographs and Related Classes

Authors: Manuel Lafond, Alitzel López Sánchez, and Weidong Luo

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In the Cluster Editing problem, sometimes known as (unweighted) Correlation Clustering, we must insert and delete a minimum number of edges to achieve a graph in which every connected component is a clique. Owing to its applications in computational biology, social network analysis, machine learning, and others, this problem has been widely studied for decades and is still undergoing active research. There exist several parameterized algorithms for general graphs, but little is known about the complexity of the problem on specific classes of graphs. Among the few important results in this direction, if only deletions are allowed, the problem can be solved in polynomial time on cographs, which are the P₄-free graphs. However, the complexity of the broader editing problem on cographs is still open. We show that even on a very restricted subclass of cographs, the problem is NP-hard, W[1]-hard when parameterized by the number p of desired clusters, and that time n^o(p/log p) is forbidden under the ETH. This shows that the editing variant is substantially harder than the deletion-only case, and that hardness holds for the many superclasses of cographs (including graphs of clique-width at most 2, perfect graphs, circle graphs, permutation graphs). On the other hand, we provide an almost tight upper bound of time n^O(p), which is a consequence of a more general n^O(cw⋅p) time algorithm, where cw is the clique-width. Given that forbidding P₄s maintains NP-hardness, we look at {P₄, C₄}-free graphs, also known as trivially perfect graphs, and provide a cubic-time algorithm for this class.
Cite as

Manuel Lafond, Alitzel López Sánchez, and Weidong Luo. Cluster Editing on Cographs and Related Classes. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 64:1-64:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lafond_et_al:LIPIcs.STACS.2025.64,
  author =	{Lafond, Manuel and L\'{o}pez S\'{a}nchez, Alitzel and Luo, Weidong},
  title =	{{Cluster Editing on Cographs and Related Classes}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{64:1--64:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.64},
  URN =		{urn:nbn:de:0030-drops-228895},
  doi =		{10.4230/LIPIcs.STACS.2025.64},
  annote =	{Keywords: Cluster editing, cographs, parameterized algorithms, clique-width, trivially perfect graphs}
}
Document
DOI: 10.4230/LIPIcs.WABI.2017.17
Forbidden Time Travel: Characterization of Time-Consistent Tree Reconciliation Maps

Authors: Nikolai Nojgaard, Manuela Geiß, Daniel Merkle, Peter F. Stadler, Nicolas Wieseke, and Marc Hellmuth

Published in: LIPIcs, Volume 88, 17th International Workshop on Algorithms in Bioinformatics (WABI 2017)

Abstract
Motivation: In the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels considerably simplifies the problem of reconciling a gene tree T with a species trees S, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure of the event labeled reconciliation problem with horizontal transfer. Results: We investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations. This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an O(|V(T)|log(|V(S)|))-time algorithm to decide whether a time-consistent reconciliation map exists. It does not require the construction of explicit timing maps, but relies entirely on the comparably easy task of checking whether a small auxiliary graph is acyclic. The algorithms are implemented in C++ using the boost graph library and are freely available at https://github.com/Nojgaard/tc-recon. Significance: The combinatorial characterization of time consistency and thus biologically feasible reconciliation is an important step towards the inference of gene family histories with hor- izontal transfer from orthology data, i.e., without presupposed gene and species trees. The fast algorithm to decide time consistency is useful in a broader context because it constitutes an attractive component for all tools that address tree reconciliation problems.
Cite as

Nikolai Nojgaard, Manuela Geiß, Daniel Merkle, Peter F. Stadler, Nicolas Wieseke, and Marc Hellmuth. Forbidden Time Travel: Characterization of Time-Consistent Tree Reconciliation Maps. In 17th International Workshop on Algorithms in Bioinformatics (WABI 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 88, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{nojgaard_et_al:LIPIcs.WABI.2017.17,
  author =	{Nojgaard, Nikolai and Gei{\ss}, Manuela and Merkle, Daniel and Stadler, Peter F. and Wieseke, Nicolas and Hellmuth, Marc},
  title =	{{Forbidden Time Travel: Characterization of Time-Consistent Tree Reconciliation Maps}},
  booktitle =	{17th International Workshop on Algorithms in Bioinformatics (WABI 2017)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-050-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{88},
  editor =	{Schwartz, Russell and Reinert, Knut},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2017.17},
  URN =		{urn:nbn:de:0030-drops-76362},
  doi =		{10.4230/LIPIcs.WABI.2017.17},
  annote =	{Keywords: Tree Reconciliation, Horizontal Gene Transfer, Reconciliation Map, Time-Consistency, History of gene families}
}
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