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Documents authored by Roy, Bodhayan

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.41
Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions

Authors: Yasushi Kawase, Bodhayan Roy, and Mohammad Azharuddin Sanpui

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
This paper explores the fair allocation of indivisible items in a multidimensional setting, motivated by the need to address fairness in complex environments where agents assess bundles according to multiple criteria. Such multidimensional settings are not merely of theoretical interest but are central to many real-world applications. For example, cloud computing resources are evaluated based on multiple criteria such as CPU cores, memory, and network bandwidth. In such cases, traditional one-dimensional fairness notions fail to capture fairness across multiple attributes. To address these challenges, we study two relaxed variants of envy-freeness: weak simultaneously envy-free up to c goods (weak sEFc) and strong simultaneously envy-free up to c goods (strong sEFc), which accommodate the multidimensionality of agents’ preferences. Under the weak notion, for every pair of agents and for each dimension, any perceived envy can be eliminated by removing, if necessary, a different set of goods from the envied agent’s allocation. In contrast, the strong version requires selecting a single set of goods whose removal from the envied bundle simultaneously eliminates envy in every dimension. We provide upper and lower bounds on the relaxation parameter c that guarantee the existence of weak or strong sEFc allocations, where these bounds are independent of the total number of items. In addition, we present algorithms for checking whether a weak or strong sEFc allocation exists. Moreover, we establish NP-hardness results for checking the existence of weak sEF1 and strong sEF1 allocations.
Cite as

Yasushi Kawase, Bodhayan Roy, and Mohammad Azharuddin Sanpui. Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kawase_et_al:LIPIcs.FSTTCS.2025.41,
  author =	{Kawase, Yasushi and Roy, Bodhayan and Sanpui, Mohammad Azharuddin},
  title =	{{Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.41},
  URN =		{urn:nbn:de:0030-drops-251210},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.41},
  annote =	{Keywords: Fair allocation, Envy-free up to one good, Multi-dimensional criteria, Linear programming, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.7
Minimum Consistent Subset in Trees and Interval Graphs

Authors: Aritra Banik, Sayani Das, Anil Maheshwari, Bubai Manna, Subhas C. Nandy, Krishna Priya K. M., Bodhayan Roy, Sasanka Roy, and Abhishek Sahu

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph G, consisting of a vertex set V(G) of size n and an edge set E(G). Each vertex in V(G) is assigned a color from the set {1,2,…, c}. The objective is to determine a subset V' ⊆ V(G) with minimum possible cardinality, such that for every vertex v ∈ V(G), at least one of its nearest neighbors in V' (measured in terms of the hop distance) shares the same color as v. The decision problem, indicating whether there exists a subset V' of cardinality at most l for some positive integer l, is known to be NP-complete even for planar graphs. In this paper, we establish that the MCS problem is NP-complete on trees. We also provide a fixed-parameter tractable (FPT) algorithm for MCS on trees parameterized by the number of colors (c) running in O(2^{6c} n^6) time, significantly improving the currently best-known algorithm whose running time is O(2^{4c} n^{2c+3}). In an effort to comprehensively understand the computational complexity of the MCS problem across different graph classes, we extend our investigation to interval graphs. We show that it remains NP-complete for interval graphs, thus enriching graph classes where MCS remains intractable.
Cite as

Aritra Banik, Sayani Das, Anil Maheshwari, Bubai Manna, Subhas C. Nandy, Krishna Priya K. M., Bodhayan Roy, Sasanka Roy, and Abhishek Sahu. Minimum Consistent Subset in Trees and Interval Graphs. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{banik_et_al:LIPIcs.FSTTCS.2024.7,
  author =	{Banik, Aritra and Das, Sayani and Maheshwari, Anil and Manna, Bubai and Nandy, Subhas C. and Priya K. M., Krishna and Roy, Bodhayan and Roy, Sasanka and Sahu, Abhishek},
  title =	{{Minimum Consistent Subset in Trees and Interval Graphs}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.7},
  URN =		{urn:nbn:de:0030-drops-221960},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.7},
  annote =	{Keywords: Nearest-Neighbor Classification, Minimum Consistent Subset, Trees, Interval Graphs, Parameterized complexity, NP-complete}
}
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.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.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.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.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.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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