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Documents authored by Pandey, Sukanya

Document
DOI: 10.4230/LIPIcs.SWAT.2024.29
Edge Multiway Cut and Node Multiway Cut Are Hard for Planar Subcubic Graphs

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

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
It is known that the weighted version of Edge Multiway Cut (also known as Multiterminal Cut) is NP-complete on planar graphs of maximum degree 3. In contrast, for the unweighted version, NP-completeness is only known for planar graphs of maximum degree 11. In fact, the complexity of unweighted Edge Multiway Cut was open for graphs of maximum degree 3 for over twenty years. We prove that the unweighted version is NP-complete even for planar graphs of maximum degree 3. As weighted Edge Multiway Cut is polynomial-time solvable for graphs of maximum degree at most 2, we have now closed the complexity gap. We also prove that (unweighted) Node Multiway Cut (both with and without deletable terminals) is NP-complete for planar graphs of maximum degree 3. By combining our results with known results, we can apply two meta-classifications on graph containment from the literature. This yields full dichotomies for all three problems on H-topological-minor-free graphs and, should H be finite, on H-subgraph-free graphs as well. Previously, such dichotomies were only implied for H-minor-free graphs.
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Matthew Johnson, Barnaby Martin, Sukanya Pandey, Daniël Paulusma, Siani Smith, and Erik Jan van Leeuwen. Edge Multiway Cut and Node Multiway Cut Are Hard for Planar Subcubic Graphs. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{johnson_et_al:LIPIcs.SWAT.2024.29,
  author =	{Johnson, Matthew and Martin, Barnaby and Pandey, Sukanya and Paulusma, Dani\"{e}l and Smith, Siani and van Leeuwen, Erik Jan},
  title =	{{Edge Multiway Cut and Node Multiway Cut Are Hard for Planar Subcubic Graphs}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.29},
  URN =		{urn:nbn:de:0030-drops-200699},
  doi =		{10.4230/LIPIcs.SWAT.2024.29},
  annote =	{Keywords: multiway cut, planar subcubic graph, complexity dichotomy, graph containment}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.6
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.
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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
DOI: 10.4230/LIPIcs.IPEC.2023.7
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.
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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
DOI: 10.4230/LIPIcs.MFCS.2023.57
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.
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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}
}
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