138 Search Results for "Bodlaender, Hans L."


Volume

LIPIcs, Volume 83

42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

MFCS 2017, August 21-25, 2017, Aalborg, Denmark

Editors: Kim G. Larsen, Hans L. Bodlaender, and Jean-Francois Raskin

Document
The Parameterised Complexity Of Integer Multicommodity Flow

Authors: Hans L. Bodlaender, Isja Mannens, Jelle J. Oostveen, Sukanya Pandey, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Path problem, have been considered. Therefore, we investigate the parameterised complexity of the general Integer Multicommodity Flow problem. We show that the decision version of this problem on directed graphs for a constant number of commodities, when the capacities are given in unary, is XNLP-complete with pathwidth as parameter and XALP-complete with treewidth as parameter. When the capacities are given in binary, the problem is NP-complete even for graphs of pathwidth at most 13. We give related results for undirected graphs. These results imply that the problem is unlikely to be fixed-parameter tractable by these parameters. In contrast, we show that the problem does become fixed-parameter tractable when weighted tree partition width (a variant of tree partition width for edge weighted graphs) is used as parameter.

Cite as

Hans L. Bodlaender, Isja Mannens, Jelle J. Oostveen, Sukanya Pandey, and Erik Jan van Leeuwen. The Parameterised Complexity Of Integer Multicommodity Flow. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 6:1-6:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2023.6,
  author =	{Bodlaender, Hans L. and Mannens, Isja and Oostveen, Jelle J. and Pandey, Sukanya and van Leeuwen, Erik Jan},
  title =	{{The Parameterised Complexity Of Integer Multicommodity Flow}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.6},
  URN =		{urn:nbn:de:0030-drops-194250},
  doi =		{10.4230/LIPIcs.IPEC.2023.6},
  annote =	{Keywords: multicommodity flow, parameterised complexity, XNLP-completeness, XALP-completeness}
}
Document
Treewidth Is NP-Complete on Cubic Graphs

Authors: Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
In this paper, we show that Treewidth is NP-complete for cubic graphs, thereby improving the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9. We add a new and simpler proof of the NP-completeness of treewidth, and show that Treewidth remains NP-complete on subcubic induced subgraphs of the infinite 3-dimensional grid.

Cite as

Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý. Treewidth Is NP-Complete on Cubic Graphs. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 7:1-7:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2023.7,
  author =	{Bodlaender, Hans L. and Bonnet, \'{E}douard and Jaffke, Lars and Knop, Du\v{s}an and Lima, Paloma T. and Milani\v{c}, Martin and Ordyniak, Sebastian and Pandey, Sukanya and Such\'{y}, Ond\v{r}ej},
  title =	{{Treewidth Is NP-Complete on Cubic Graphs}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.7},
  URN =		{urn:nbn:de:0030-drops-194263},
  doi =		{10.4230/LIPIcs.IPEC.2023.7},
  annote =	{Keywords: Treewidth, cubic graphs, degree, NP-completeness}
}
Document
Complexity Framework for Forbidden Subgraphs III: When Problems Are Tractable on Subcubic Graphs

Authors: Matthew Johnson, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Siani Smith, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
For any finite set ℋ = {H_1,…,H_p} of graphs, a graph is ℋ-subgraph-free if it does not contain any of H_1,…,H_p as a subgraph. In recent work, meta-classifications have been studied: these show that if graph problems satisfy certain prescribed conditions, their complexity can be classified on classes of ℋ-subgraph-free graphs. We continue this work and focus on problems that have polynomial-time solutions on classes that have bounded treewidth or maximum degree at most 3 and examine their complexity on H-subgraph-free graph classes where H is a connected graph. With this approach, we obtain comprehensive classifications for (Independent) Feedback Vertex Set, Connected Vertex Cover, Colouring and Matching Cut. This resolves a number of open problems. We highlight that, to establish that Independent Feedback Vertex Set belongs to this collection of problems, we first show that it can be solved in polynomial time on graphs of maximum degree 3. We demonstrate that, with the exception of the complete graph on four vertices, each graph in this class has a minimum size feedback vertex set that is also an independent set.

Cite as

Matthew Johnson, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Siani Smith, and Erik Jan van Leeuwen. Complexity Framework for Forbidden Subgraphs III: When Problems Are Tractable on Subcubic Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 57:1-57:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{johnson_et_al:LIPIcs.MFCS.2023.57,
  author =	{Johnson, Matthew and Martin, Barnaby and Pandey, Sukanya and Paulusma, Dani\"{e}l and Smith, Siani and van Leeuwen, Erik Jan},
  title =	{{Complexity Framework for Forbidden Subgraphs III: When Problems Are Tractable on Subcubic Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.57},
  URN =		{urn:nbn:de:0030-drops-185914},
  doi =		{10.4230/LIPIcs.MFCS.2023.57},
  annote =	{Keywords: forbidden subgraphs, independent feedback vertex set, treewidth}
}
Document
Track A: Algorithms, Complexity and Games
Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters

Authors: Hans L. Bodlaender, Carla Groenland, and Michał Pilipczuk

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows: - Binary CSP parameterized by the vertex cover number is W[3]-complete. More generally, for every positive integer d, Binary CSP parameterized by the size of a modulator to a treedepth-d graph is W[2d+1]-complete. This provides a new family of natural problems that are complete for odd levels of the W-hierarchy. - We introduce a new complexity class XSLP, defined so that Binary CSP parameterized by treedepth is complete for this class. We provide two equivalent characterizations of XSLP: the first one relates XSLP to a model of an alternating Turing machine with certain restrictions on conondeterminism and space complexity, while the second one links XSLP to the problem of model-checking first-order logic with suitably restricted universal quantification. Interestingly, the proof of the machine characterization of XSLP uses the concept of universal trees, which are prominently featured in the recent work on parity games. - We describe a new complexity hierarchy sandwiched between the W-hierarchy and the A-hierarchy: For every odd t, we introduce a parameterized complexity class S[t] with W[t] ⊆ S[t] ⊆ A[t], defined using a parameter that interpolates between the vertex cover number and the treedepth. We expect that many of the studied classes will be useful in the future for pinpointing the complexity of various structural parameterizations of graph problems.

Cite as

Hans L. Bodlaender, Carla Groenland, and Michał Pilipczuk. Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 27:1-27:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bodlaender_et_al:LIPIcs.ICALP.2023.27,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Pilipczuk, Micha{\l}},
  title =	{{Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{27:1--27:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.27},
  URN =		{urn:nbn:de:0030-drops-180798},
  doi =		{10.4230/LIPIcs.ICALP.2023.27},
  annote =	{Keywords: Parameterized Complexity, Constraint Satisfaction Problems, Binary CSP, List Coloring, Vertex Cover, Treedepth, W-hierarchy}
}
Document
On the Complexity of Problems on Tree-Structured Graphs

Authors: Hans L. Bodlaender, Carla Groenland, Hugo Jacob, Marcin Pilipczuk, and Michał Pilipczuk

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)


Abstract
In this paper, we introduce a new class of parameterized problems, which we call XALP: the class of all parameterized problems that can be solved in f(k)n^O(1) time and f(k)log n space on a non-deterministic Turing Machine with access to an auxiliary stack (with only top element lookup allowed). Various natural problems on "tree-structured graphs" are complete for this class: we show that List Coloring and All-or-Nothing Flow parameterized by treewidth are XALP-complete. Moreover, Independent Set and Dominating Set parameterized by treewidth divided by log n, and Max Cut parameterized by cliquewidth are also XALP-complete. Besides finding a "natural home" for these problems, we also pave the road for future reductions. We give a number of equivalent characterisations of the class XALP, e.g., XALP is the class of problems solvable by an Alternating Turing Machine whose runs have tree size at most f(k)n^O(1) and use f(k)log n space. Moreover, we introduce "tree-shaped" variants of Weighted CNF-Satisfiability and Multicolor Clique that are XALP-complete.

Cite as

Hans L. Bodlaender, Carla Groenland, Hugo Jacob, Marcin Pilipczuk, and Michał Pilipczuk. On the Complexity of Problems on Tree-Structured Graphs. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 6:1-6:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2022.6,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Jacob, Hugo and Pilipczuk, Marcin and Pilipczuk, Micha{\l}},
  title =	{{On the Complexity of Problems on Tree-Structured Graphs}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.6},
  URN =		{urn:nbn:de:0030-drops-173626},
  doi =		{10.4230/LIPIcs.IPEC.2022.6},
  annote =	{Keywords: Parameterized Complexity, Treewidth, XALP, XNLP}
}
Document
On the Parameterized Complexity of Computing Tree-Partitions

Authors: Hans L. Bodlaender, Carla Groenland, and Hugo Jacob

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)


Abstract
We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an n-vertex graph G and an integer k, constructs a tree-partition of width O(k⁷) for G or reports that G has tree-partition width more than k, in time k^O(1) n². We can improve slightly on the approximation factor by sacrificing the dependence on k, or on n. On the other hand, we show the problem of computing tree-partition-width exactly is XALP-complete, which implies that it is W[t]-hard for all t. We deduce XALP-completeness of the problem of computing the domino treewidth. Finally, we adapt some known results on the parameter tree-partition-width and the topological minor relation, and use them to compare tree-partition-width to tree-cut width.

Cite as

Hans L. Bodlaender, Carla Groenland, and Hugo Jacob. On the Parameterized Complexity of Computing Tree-Partitions. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 7:1-7:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2022.7,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Jacob, Hugo},
  title =	{{On the Parameterized Complexity of Computing Tree-Partitions}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.7},
  URN =		{urn:nbn:de:0030-drops-173633},
  doi =		{10.4230/LIPIcs.IPEC.2022.7},
  annote =	{Keywords: Parameterized algorithms, Tree partitions, tree-partition-width, Treewidth, Domino Treewidth, Approximation Algorithms, Parameterized Complexity}
}
Document
XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure

Authors: Hans L. Bodlaender, Carla Groenland, Hugo Jacob, Lars Jaffke, and Paloma T. Lima

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)


Abstract
In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing W[1]-hardness proofs for these problems, since XNLP-hardness implies W[t]-hardness for all t. It also indicates, via a conjecture by Pilipczuk and Wrochna [ToCT 2018], that any XP algorithm for such problems is likely to require XP space. In particular, we show XNLP-completeness for natural problems parameterized by pathwidth, linear clique-width, and linear mim-width. The problems we consider are Independent Set, Dominating Set, Odd Cycle Transversal, (q-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set, Capacitated (Red-Blue) Dominating Set, and Bipartite Bandwidth.

Cite as

Hans L. Bodlaender, Carla Groenland, Hugo Jacob, Lars Jaffke, and Paloma T. Lima. XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 8:1-8:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2022.8,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Jacob, Hugo and Jaffke, Lars and Lima, Paloma T.},
  title =	{{XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.8},
  URN =		{urn:nbn:de:0030-drops-173640},
  doi =		{10.4230/LIPIcs.IPEC.2022.8},
  annote =	{Keywords: parameterized complexity, XNLP, linear clique-width, W-hierarchy, pathwidth, linear mim-width, bandwidth}
}
Document
List Colouring Trees in Logarithmic Space

Authors: Hans L. Bodlaender, Carla Groenland, and Hugo Jacob

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)


Abstract
We show that List Colouring can be solved on n-vertex trees by a deterministic Turing machine using O(log n) bits on the worktape. Given an n-vertex graph G = (V,E) and a list L(v) ⊆ {1,… ,n} of available colours for each v ∈ V, a list colouring for G is a proper colouring c such that c(v) ∈ L(v) for all v.

Cite as

Hans L. Bodlaender, Carla Groenland, and Hugo Jacob. List Colouring Trees in Logarithmic Space. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 24:1-24:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bodlaender_et_al:LIPIcs.ESA.2022.24,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Jacob, Hugo},
  title =	{{List Colouring Trees in Logarithmic Space}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.24},
  URN =		{urn:nbn:de:0030-drops-169620},
  doi =		{10.4230/LIPIcs.ESA.2022.24},
  annote =	{Keywords: List colouring, trees, space complexity, logspace, graph algorithms, tree-partition-width}
}
Document
Parameterized Complexities of Dominating and Independent Set Reconfiguration

Authors: Hans L. Bodlaender, Carla Groenland, and Céline M. F. Swennenhuis

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)


Abstract
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves and XNL-complete when a maximum length 𝓁 for the sequence is given in binary in the input. The problems are known to be XNLP-complete when 𝓁 is given in unary instead, and W[1]- and W[2]-hard respectively when 𝓁 is also a parameter. We complete the picture by showing membership in those classes. Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.

Cite as

Hans L. Bodlaender, Carla Groenland, and Céline M. F. Swennenhuis. Parameterized Complexities of Dominating and Independent Set Reconfiguration. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 9:1-9:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2021.9,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Swennenhuis, C\'{e}line M. F.},
  title =	{{Parameterized Complexities of Dominating and Independent Set Reconfiguration}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.9},
  URN =		{urn:nbn:de:0030-drops-153920},
  doi =		{10.4230/LIPIcs.IPEC.2021.9},
  annote =	{Keywords: Parameterized complexity, independent set reconfiguration, dominating set reconfiguration, W-hierarchy, XL, XNL, XNLP}
}
Document
Parameterized Complexity of Scheduling Chains of Jobs with Delays

Authors: Hans L. Bodlaender and Marieke van der Wegen

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)


Abstract
In this paper, we consider the parameterized complexity of the following scheduling problem. We must schedule a number of jobs on m machines, where each job has unit length, and the graph of precedence constraints consists of a set of chains. Each precedence constraint is labelled with an integer that denotes the exact (or minimum) delay between the jobs. We study different cases; delays can be given in unary and in binary, and the case that we have a single machine is discussed separately. We consider the complexity of this problem parameterized by the number of chains, and by the thickness of the instance, which is the maximum number of chains whose intervals between release date and deadline overlap. We show that this scheduling problem with exact delays in unary is W[t]-hard for all t, when parameterized by the thickness, even when we have a single machine (m = 1). When parameterized by the number of chains, this problem is W[1]-complete when we have a single or a constant number of machines, and W[2]-complete when the number of machines is a variable. The problem with minimum delays, given in unary, parameterized by the number of chains (and as a simple corollary, also when parameterized by the thickness) is W[1]-hard for a single or a constant number of machines, and W[2]-hard when the number of machines is variable. With a dynamic programming algorithm, one can show membership in XP for exact and minimum delays in unary, for any number of machines, when parameterized by thickness or number of chains. For a single machine, with exact delays in binary, parameterized by the number of chains, membership in XP can be shown with branching and solving a system of difference constraints. For all other cases for delays in binary, membership in XP is open.

Cite as

Hans L. Bodlaender and Marieke van der Wegen. Parameterized Complexity of Scheduling Chains of Jobs with Delays. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 4:1-4:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2020.4,
  author =	{Bodlaender, Hans L. and van der Wegen, Marieke},
  title =	{{Parameterized Complexity of Scheduling Chains of Jobs with Delays}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.4},
  URN =		{urn:nbn:de:0030-drops-133075},
  doi =		{10.4230/LIPIcs.IPEC.2020.4},
  annote =	{Keywords: Scheduling, parameterized complexity}
}
Document
Weighted Tiling Systems for Graphs: Evaluation Complexity

Authors: C. Aiswarya and Paul Gastin

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)


Abstract
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of every node belongs to a set of permissible tiles, and assigns a weight accordingly. The weight of a labeling is the semiring-product of the weights assigned to the nodes, and the weight of the graph is the semiring-sum of the weights of labelings. We show that we can model interesting algorithmic questions using this formalism - like computing the clique number of a graph or computing the permanent of a matrix. The evaluation problem is, given a weighted tiling system and a graph, to compute the weight of the graph. We study the complexity of the evaluation problem and give tight upper and lower bounds for several commutative semirings. Further we provide an efficient evaluation algorithm if the input graph is of bounded tree-width.

Cite as

C. Aiswarya and Paul Gastin. Weighted Tiling Systems for Graphs: Evaluation Complexity. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{aiswarya_et_al:LIPIcs.FSTTCS.2020.34,
  author =	{Aiswarya, C. and Gastin, Paul},
  title =	{{Weighted Tiling Systems for Graphs: Evaluation Complexity}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.34},
  URN =		{urn:nbn:de:0030-drops-132753},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.34},
  annote =	{Keywords: Weighted graph tiling, tiling automata, Evaluation, Complexity, Tree-width}
}
Document
Typical Sequences Revisited - Computing Width Parameters of Graphs

Authors: Hans L. Bodlaender, Lars Jaffke, and Jan Arne Telle

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
In this work, we give a structural lemma on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP 1991] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth. The lemma addresses a runtime bottleneck in those algorithms but so far it does not lead to asymptotically faster algorithms. However, we apply the lemma to show that the cutwidth and the modified cutwidth of series parallel digraphs can be computed in ?(n²) time.

Cite as

Hans L. Bodlaender, Lars Jaffke, and Jan Arne Telle. Typical Sequences Revisited - Computing Width Parameters of Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 57:1-57:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bodlaender_et_al:LIPIcs.STACS.2020.57,
  author =	{Bodlaender, Hans L. and Jaffke, Lars and Telle, Jan Arne},
  title =	{{Typical Sequences Revisited - Computing Width Parameters of Graphs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.57},
  URN =		{urn:nbn:de:0030-drops-119189},
  doi =		{10.4230/LIPIcs.STACS.2020.57},
  annote =	{Keywords: typical sequences, treewidth, series parallel digraphs, cutwidth, modified cutwidth}
}
Document
Invited Paper
From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper)

Authors: Stefan Milius

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
This extended abstract first presents a new category theoretic approach to equationally axiomatizable classes of algebras. This approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered algebras, continuous algebras, quantitative algebras, nominal algebras, or profinite algebras. We present a generic HSP theorem and a sound and complete equational logic, which encompass numerous flavors of equational axiomizations studied in the literature. In addition, we use the generic HSP theorem as a key ingredient to obtain Eilenberg-type correspondences yielding algebraic characterizations of properties of regular machine behaviours. When instantiated for orbit-finite nominal monoids, the generic HSP theorem yields a crucial step for the proof of the first Eilenberg-type variety theorem for data languages.

Cite as

Stefan Milius. From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 2:1-2:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{milius:LIPIcs.CALCO.2019.2,
  author =	{Milius, Stefan},
  title =	{{From Equational Specifications of Algebras with Structure to Varieties of Data Languages}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{2:1--2:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.2},
  URN =		{urn:nbn:de:0030-drops-114309},
  doi =		{10.4230/LIPIcs.CALCO.2019.2},
  annote =	{Keywords: Birkhoff theorem, Equational logic, Eilenberg theorem, Data languages}
}
Document
Parameterized Complexity of Fair Vertex Evaluation Problems

Authors: Dušan Knop, Tomáš Masařík, and Tomáš Toufar

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists a solution of a certain quality, where we use size as a quality measure. In this work, we are changing the measure to the fair measure (cf. Lin and Sahni [Li-Shin Lin and Sartaj Sahni, 1989]). The fair measure of a set of vertices S is (at most) k if the number of neighbors in the set S of any vertex (in the input graph) does not exceed k. One possible way to study graph problems is by defining the property in a certain logic. For a given objective, an evaluation problem is to find a set (of vertices) that simultaneously minimizes the assumed measure and satisfies an appropriate formula. More formally, we study the {MSO} Fair Vertex Evaluation, where the graph-theoretic property is described by an {MSO} formula. In the presented paper we show that there is an FPT algorithm for the {MSO} Fair Vertex Evaluation problem for formulas with one free variable parameterized by the twin cover number of the input graph and the size of the formula. One may define an extended variant of {MSO} Fair Vertex Evaluation for formulas with l free variables; here we measure a maximum number of neighbors in each of the l sets. However, such variant is {W[1]}-hard for parameter l even on graphs with twin cover one. Furthermore, we study the Fair Vertex Cover (Fair VC) problem. Fair VC is among the simplest problems with respect to the demanded property (i.e., the rest forms an edgeless graph). On the negative side, Fair VC is {W[1]}-hard when parameterized by both treedepth and feedback vertex set of the input graph. On the positive side, we provide an FPT algorithm for the parameter modular width.

Cite as

Dušan Knop, Tomáš Masařík, and Tomáš Toufar. Parameterized Complexity of Fair Vertex Evaluation Problems. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{knop_et_al:LIPIcs.MFCS.2019.33,
  author =	{Knop, Du\v{s}an and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Toufar, Tom\'{a}\v{s}},
  title =	{{Parameterized Complexity of Fair Vertex Evaluation Problems}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.33},
  URN =		{urn:nbn:de:0030-drops-109775},
  doi =		{10.4230/LIPIcs.MFCS.2019.33},
  annote =	{Keywords: Fair objective, metatheorem, fair vertex cover, twin cover, modular width}
}
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