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Documents authored by Nandy, Subhas C.

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.FSTTCS.2022.18
Half-Guarding Weakly-Visible Polygons and Terrains

Authors: Nandhana Duraisamy, Hannah Miller Hillberg, Ramesh K. Jallu, Erik Krohn, Anil Maheshwari, Subhas C. Nandy, and Alex Pahlow

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
We consider a variant of the art gallery problem where all guards are limited to seeing 180degree. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for vertex guarding the vertices of a weakly-visible polygon with half-guards. We extend this to vertex guarding the boundary of a weakly-visible polygon with half-guards. We also show NP-hardness for vertex guarding a weakly-visible polygon with half-guards. Lastly, we show that the orientation of half-guards is critical in terrain guarding. Depending on the orientation of the half-guards, the problem is either very easy (polynomial time solvable) or very hard (NP-hard).
Cite as

Nandhana Duraisamy, Hannah Miller Hillberg, Ramesh K. Jallu, Erik Krohn, Anil Maheshwari, Subhas C. Nandy, and Alex Pahlow. Half-Guarding Weakly-Visible Polygons and Terrains. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{duraisamy_et_al:LIPIcs.FSTTCS.2022.18,
  author =	{Duraisamy, Nandhana and Hillberg, Hannah Miller and Jallu, Ramesh K. and Krohn, Erik and Maheshwari, Anil and Nandy, Subhas C. and Pahlow, Alex},
  title =	{{Half-Guarding Weakly-Visible Polygons and Terrains}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.18},
  URN =		{urn:nbn:de:0030-drops-174103},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.18},
  annote =	{Keywords: Art Gallery Problem, Approximation Algorithm, NP-Hardness, Monotone Polygons, Half-Guards}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.24
Discriminating Codes in Geometric Setups

Authors: Sanjana Dey, Florent Foucaud, Subhas C. Nandy, and Arunabha Sen

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

Abstract
We study two geometric variations of the discriminating code problem. In the discrete version, a finite set of points P and a finite set of objects S are given in ℝ^d. The objective is to choose a subset S^* ⊆ S of minimum cardinality such that the subsets S_i^* ⊆ S^* covering p_i, satisfy S_i^* ≠ ∅ for each i = 1,2,…, n, and S_i^* ≠ S_j^* for each pair (i,j), i ≠ j. In the continuous version, the solution set S^* can be chosen freely among a (potentially infinite) class of allowed geometric objects. In the 1-dimensional case (d = 1), the points are placed on some fixed-line L, and the objects in S are finite segments of L (called intervals). We show that the discrete version of this problem is NP-complete. This is somewhat surprising as the continuous version is known to be polynomial-time solvable. This is also in contrast with most geometric covering problems, which are usually polynomial-time solvable in 1D. We then design a polynomial-time 2-approximation algorithm for the 1-dimensional discrete case. We also design a PTAS for both discrete and continuous cases when the intervals are all required to have the same length. We then study the 2-dimensional case (d = 2) for axis-parallel unit square objects. We show that both continuous and discrete versions are NP-hard, and design polynomial-time approximation algorithms with factors 4+ε and 32+ε, respectively (for every fixed ε > 0).
Cite as

Sanjana Dey, Florent Foucaud, Subhas C. Nandy, and Arunabha Sen. Discriminating Codes in Geometric Setups. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dey_et_al:LIPIcs.ISAAC.2020.24,
  author =	{Dey, Sanjana and Foucaud, Florent and Nandy, Subhas C. and Sen, Arunabha},
  title =	{{Discriminating Codes in Geometric Setups}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{24:1--24:16},
  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.2020.24},
  URN =		{urn:nbn:de:0030-drops-133686},
  doi =		{10.4230/LIPIcs.ISAAC.2020.24},
  annote =	{Keywords: Discriminating code, Approximation algorithm, Segment stabbing, Geometric Hitting set}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.336
On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model

Authors: Arijit Bishnu, Amit Chakrabarti, Subhas C. Nandy, and Sandeep Sen

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
In this paper, we study the maximum density, threshold and emptiness queries for intervals in the streaming model. The input is a stream S of n points in the real line R and a floating closed interval W of width alpha. The specific problems we consider in this paper are as follows. - Maximum density: find a placement of W in R containing the maximum number of points of S. - Threshold query: find a placement of W in R, if it exists, that contains at least Delta elements of S. - Emptiness query: find, if possible, a placement of W within the extent of S so that the interior of W does not contain any element of S. The stream S, being huge, does not fit into main memory and can be read sequentially at most a constant number of times, usually once. The problems studied here in the geometric setting have relations to frequency estimation and heavy hitter identification in a stream of data. We provide lower bounds and results on trade-off between extra space and quality of solution. We also discuss generalizations for the higher dimensional variants for a few cases.
Cite as

Arijit Bishnu, Amit Chakrabarti, Subhas C. Nandy, and Sandeep Sen. On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 336-349, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bishnu_et_al:LIPIcs.FSTTCS.2015.336,
  author =	{Bishnu, Arijit and Chakrabarti, Amit and Nandy, Subhas C. and Sen, Sandeep},
  title =	{{On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{336--349},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.336},
  URN =		{urn:nbn:de:0030-drops-56488},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.336},
  annote =	{Keywords: Density, threshold, emptiness queries, interval queries, streaming model, heavy hitter, frequency estimation}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.510
Minimum Enclosing Circle with Few Extra Variables

Authors: Minati De, Subhas C. Nandy, and Sasanka Roy

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
Asano et al. [JoCG 2011] proposed an open problem of computing the minimum enclosing circle of a set of n points in R^2 given in a read-only array in sub-quadratic time. We show that Megiddo's prune and search algorithm for computing the minimum radius circle enclosing the given points can be tailored to work in a read-only environment in O(n^{1+epsilon}) time using O(log n) extra space, where epsilon is a positive constant less than 1. As a warm-up, we first solve the same problem in an in-place setup in linear time with O(1) extra space.
Cite as

Minati De, Subhas C. Nandy, and Sasanka Roy. Minimum Enclosing Circle with Few Extra Variables. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 510-521, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{de_et_al:LIPIcs.FSTTCS.2012.510,
  author =	{De, Minati and Nandy, Subhas C. and Roy, Sasanka},
  title =	{{Minimum Enclosing Circle with Few Extra Variables}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{510--521},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.510},
  URN =		{urn:nbn:de:0030-drops-38855},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.510},
  annote =	{Keywords: Minimum enclosing circle, space-efficient algorithm, prune-and-search}
}
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