5 Search Results for "Roy, Bodhayan"

Document
DOI: 10.4230/LIPIcs.SoCG.2021.7
Complexity of Maximum Cut on Interval Graphs

Authors: Ranendu Adhikary, Kaustav Bose, Satwik Mukherjee, and Bodhayan Roy

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.
Cite as

Ranendu Adhikary, Kaustav Bose, Satwik Mukherjee, and Bodhayan Roy. Complexity of Maximum Cut on Interval Graphs. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 7:1-7:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{adhikary_et_al:LIPIcs.SoCG.2021.7,
  author =	{Adhikary, Ranendu and Bose, Kaustav and Mukherjee, Satwik and Roy, Bodhayan},
  title =	{{Complexity of Maximum Cut on Interval Graphs}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{7:1--7:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.7},
  URN =		{urn:nbn:de:0030-drops-138067},
  doi =		{10.4230/LIPIcs.SoCG.2021.7},
  annote =	{Keywords: Maximum cut, Interval graph, NP-complete}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.29
Colouring Polygon Visibility Graphs and Their Generalizations

Authors: James Davies, Tomasz Krawczyk, Rose McCarty, and Bartosz Walczak

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number ω has chromatic number at most 3⋅4^{ω-1}. The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.
Cite as

James Davies, Tomasz Krawczyk, Rose McCarty, and Bartosz Walczak. Colouring Polygon Visibility Graphs and Their Generalizations. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{davies_et_al:LIPIcs.SoCG.2021.29,
  author =	{Davies, James and Krawczyk, Tomasz and McCarty, Rose and Walczak, Bartosz},
  title =	{{Colouring Polygon Visibility Graphs and Their Generalizations}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.29},
  URN =		{urn:nbn:de:0030-drops-138281},
  doi =		{10.4230/LIPIcs.SoCG.2021.29},
  annote =	{Keywords: Visibility graphs, \chi-boundedness, pseudoline arrangements, ordered graphs}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.7
Algorithms and Complexity for Geodetic Sets on Planar and Chordal Graphs

Authors: Dibyayan Chakraborty, Sandip Das, Florent Foucaud, Harmender Gahlawat, Dimitri Lajou, and Bodhayan Roy

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
We study the complexity of finding the geodetic number on subclasses of planar graphs and chordal graphs. A set S of vertices of a graph G is a geodetic set if every vertex of G lies in a shortest path between some pair of vertices of S. The Minimum Geodetic Set (MGS) problem is to find a geodetic set with minimum cardinality of a given graph. The problem is known to remain NP-hard on bipartite graphs, chordal graphs, planar graphs and subcubic graphs. We first study MGS on restricted classes of planar graphs: we design a linear-time algorithm for MGS on solid grids, improving on a 3-approximation algorithm by Chakraborty et al. (CALDAM, 2020) and show that MGS remains NP-hard even for subcubic partial grids of arbitrary girth. This unifies some results in the literature. We then turn our attention to chordal graphs, showing that MGS is fixed parameter tractable for inputs of this class when parameterized by their treewidth (which equals the clique number minus one). This implies a linear-time algorithm for k-trees, for fixed k. Then, we show that MGS is NP-hard on interval graphs, thereby answering a question of Ekim et al. (LATIN, 2012). As interval graphs are very constrained, to prove the latter result we design a rather sophisticated reduction technique to work around their inherent linear structure.
Cite as

Dibyayan Chakraborty, Sandip Das, Florent Foucaud, Harmender Gahlawat, Dimitri Lajou, and Bodhayan Roy. Algorithms and Complexity for Geodetic Sets on Planar and Chordal Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2020.7,
  author =	{Chakraborty, Dibyayan and Das, Sandip and Foucaud, Florent and Gahlawat, Harmender and Lajou, Dimitri and Roy, Bodhayan},
  title =	{{Algorithms and Complexity for Geodetic Sets on Planar and Chordal Graphs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.7},
  URN =		{urn:nbn:de:0030-drops-133516},
  doi =		{10.4230/LIPIcs.ISAAC.2020.7},
  annote =	{Keywords: Geodetic set, Planar graph, Chordal graph, Interval graph, FPT algorithm}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2017.19
FO Model Checking of Geometric Graphs

Authors: Petr Hlineny, Filip Pokrývka, and Bodhayan Roy

Published in: LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Abstract
Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking of dense classes of graphs or other structures. We study the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs). We obtain new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs. These results use the FPT algorithm by Gajarský et al. for FO model checking of posets of bounded width. We also complement the tractability results by related hardness reductions.
Cite as

Petr Hlineny, Filip Pokrývka, and Bodhayan Roy. FO Model Checking of Geometric Graphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hlineny_et_al:LIPIcs.IPEC.2017.19,
  author =	{Hlineny, Petr and Pokr\'{y}vka, Filip and Roy, Bodhayan},
  title =	{{FO Model Checking of Geometric Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Lokshtanov, Daniel and Nishimura, Naomi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.19},
  URN =		{urn:nbn:de:0030-drops-85597},
  doi =		{10.4230/LIPIcs.IPEC.2017.19},
  annote =	{Keywords: first-order logic, model checking, fixed-parameter tractability, intersection graphs, visibility graphs}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2017.21
On Colourability of Polygon Visibility Graphs

Authors: Onur Cagirici, Petr Hlinený, and Bodhayan Roy

Published in: LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

Abstract
We study the problem of colouring the visibility graphs of polygons. In particular, we provide a polynomial algorithm for 4-colouring of the polygon visibility graphs, and prove that the 6- colourability question is already NP-complete for them.
Cite as

Onur Cagirici, Petr Hlinený, and Bodhayan Roy. On Colourability of Polygon Visibility Graphs. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cagirici_et_al:LIPIcs.FSTTCS.2017.21,
  author =	{Cagirici, Onur and Hlinen\'{y}, Petr and Roy, Bodhayan},
  title =	{{On Colourability of Polygon Visibility Graphs}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Lokam, Satya and Ramanujam, R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.21},
  URN =		{urn:nbn:de:0030-drops-83814},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.21},
  annote =	{Keywords: polygon visibility graph, graph coloring, NP-completeness}
}
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