3 Search Results for "Jallu, Ramesh K."

Document
DOI: 10.4230/LIPIcs.STACS.2025.73
Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position

Authors: Anastasiia Tkachenko and Haitao Wang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Given a set P of n points in the plane, its unit-disk graph G(P) is a graph with P as its vertex set such that two points of P are connected by an edge if their (Euclidean) distance is at most 1. We consider several classical problems on G(P) in a special setting when points of P are in convex position. These problems are all NP-hard in the general case. We present efficient algorithms for these problems under the convex position assumption. ● For the problem of finding the smallest dominating set of G(P), we present an O(knlog n) time algorithm, where k is the smallest dominating set size. We also consider the weighted case in which each point of P has a weight and the goal is to find a dominating set in G(P) with minimum total weight; our algorithm runs in O(n³log² n) time. In particular, for a given k, our algorithm can compute in O(kn²log² n) time a minimum weight dominating set of size at most k (if it exists). ● For the discrete k-center problem, which is to find a subset of k points in P (called centers) for a given k, such that the maximum distance between any point in P and its nearest center is minimized. We present an algorithm that solves the problem in O(min{n^{4/3}log n+knlog² n,k² nlog²n}) time, which is O(n²log² n) in the worst case when k = Θ(n). For comparison, the runtime of the current best algorithm for the continuous version of the problem where centers can be anywhere in the plane is O(n³ log n). ● For the problem of finding a maximum independent set in G(P), we give an algorithm of O(n^{7/2}) time and another randomized algorithm of O(n^{37/11}) expected time, which improve the previous best result of O(n⁶log n) time. Our algorithms can be extended to compute a maximum-weight independent set in G(P) with the same time complexities when points of P have weights. - If we are looking for an (unweighted) independent set of size 3, we derive an algorithm of O(nlog n) time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position). - If points of P have weights and are not necessarily in convex position, we present an algorithm that can find a maximum-weight independent set of size 3 in O(n^{5/3+δ}) time for an arbitrarily small constant δ > 0. By slightly modifying the algorithm, a maximum-weight clique of size 3 can also be found within the same time complexity. ● For the dispersion problem, which is to find a subset of k points from P for a given k, such that the minimum pairwise distance of the points in the subset is maximized. We present an algorithm of O(n^{7/2}log n) time and another randomized algorithm of O(n^{37/11}log n) expected time, which improve the previous best result of O(n⁶) time. - If k = 3, we present an algorithm of O(nlog² n) time and another randomized algorithm of O(nlog n) expected time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position).
Cite as

Anastasiia Tkachenko and Haitao Wang. Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tkachenko_et_al:LIPIcs.STACS.2025.73,
  author =	{Tkachenko, Anastasiia and Wang, Haitao},
  title =	{{Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.73},
  URN =		{urn:nbn:de:0030-drops-228982},
  doi =		{10.4230/LIPIcs.STACS.2025.73},
  annote =	{Keywords: Dominating set, k-center, geometric set cover, independent set, clique, vertex cover, unit-disk graphs, convex position, dispersion, maximally separated sets}
}
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.GIScience.2021.II.10
Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

Authors: Ankush Acharyya, Ramesh K. Jallu, Maarten Löffler, Gert G.T. Meijer, Maria Saumell, Rodrigo I. Silveira, and Frank Staals

Published in: LIPIcs, Volume 208, 11th International Conference on Geographic Information Science (GIScience 2021) - Part II

Abstract
An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains.
Cite as

Ankush Acharyya, Ramesh K. Jallu, Maarten Löffler, Gert G.T. Meijer, Maria Saumell, Rodrigo I. Silveira, and Frank Staals. Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{acharyya_et_al:LIPIcs.GIScience.2021.II.10,
  author =	{Acharyya, Ankush and Jallu, Ramesh K. and L\"{o}ffler, Maarten and Meijer, Gert G.T. and Saumell, Maria and Silveira, Rodrigo I. and Staals, Frank},
  title =	{{Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-208-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{208},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.10},
  URN =		{urn:nbn:de:0030-drops-147697},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.10},
  annote =	{Keywords: Digital elevation model, Triangulated irregular network, Viewshed complexity}
}
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