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Documents authored by Acharya, Aditya

Document
DOI: 10.4230/LIPIcs.WADS.2025.3
Support Vector Machines in the Hilbert Geometry

Authors: Aditya Acharya, Auguste H. Gezalyan, Julian Vanecek, David M. Mount, and Sunil Arya

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Support Vector Machines (SVMs) are a class of classification models in machine learning that are based on computing a maximum-margin separator between two sets of points. The SVM problem has been heavily studied for Euclidean geometry and for a number of kernels. In this paper, we consider the linear SVM problem in the Hilbert metric, a non-Euclidean geometry defined over a convex body. We present efficient algorithms for computing the SVM classifier for a set of n points in the Hilbert metric defined by convex polygons in the plane and convex polytopes in d-dimensional space. We also consider the problems in the related Funk distance.
Cite as

Aditya Acharya, Auguste H. Gezalyan, Julian Vanecek, David M. Mount, and Sunil Arya. Support Vector Machines in the Hilbert Geometry. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{acharya_et_al:LIPIcs.WADS.2025.3,
  author =	{Acharya, Aditya and Gezalyan, Auguste H. and Vanecek, Julian and Mount, David M. and Arya, Sunil},
  title =	{{Support Vector Machines in the Hilbert Geometry}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.3},
  URN =		{urn:nbn:de:0030-drops-242348},
  doi =		{10.4230/LIPIcs.WADS.2025.3},
  annote =	{Keywords: Support vector machines, Hilbert geometry, linear classification, machine learning, LP-type problems}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.4
Evolving Distributions Under Local Motion

Authors: Aditya Acharya and David M. Mount

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Geometric data sets that arise in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies over time due to the unseen actions of an evolver, which makes small changes to the data. An algorithm probes the current state through an oracle, and the objective is to maintain a hypothesis of the data set’s current state that is close to its actual state at all times. In this paper, we apply this framework to maintaining a set of n point objects in motion in d-dimensional Euclidean space. To model the uncertainty in the object locations, both the ground truth and hypothesis are based on spatial probability distributions, and the distance between them is measured by the Kullback-Leibler divergence (relative entropy). We introduce a simple and intuitive motion model in which, with each time step, the distance that any object can move is a fraction of the distance to its nearest neighbor. We present an algorithm that, in steady state, guarantees a distance of O(n) between the true and hypothesized placements. We also show that for any algorithm in this model, there is an evolver that can generate a distance of Ω(n), implying that our algorithm is asymptotically optimal.
Cite as

Aditya Acharya and David M. Mount. Evolving Distributions Under Local Motion. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{acharya_et_al:LIPIcs.WADS.2025.4,
  author =	{Acharya, Aditya and Mount, David M.},
  title =	{{Evolving Distributions Under Local Motion}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.4},
  URN =		{urn:nbn:de:0030-drops-242357},
  doi =		{10.4230/LIPIcs.WADS.2025.4},
  annote =	{Keywords: Evolving data, tracking, imprecise points, local-motion model, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.FUN.2016.1
2048 Without New Tiles Is Still Hard

Authors: Ahmed Abdelkader, Aditya Acharya, and Philip Dasler

Published in: LIPIcs, Volume 49, 8th International Conference on Fun with Algorithms (FUN 2016)

Abstract
We study the computational complexity of a variant of the popular 2048 game in which no new tiles are generated after each move. As usual, instances are defined on rectangular boards of arbitrary size. We consider the natural decision problems of achieving a given constant tile value, score or number of moves. We also consider approximating the maximum achievable value for these three objectives. We prove all these problems are NP-hard by a reduction from 3SAT. Furthermore, we consider potential extensions of these results to a similar variant of the Threes! game. To this end, we report on a peculiar motion pattern, that is not possible in 2048, which we found much harder to control by similar board designs.
Cite as

Ahmed Abdelkader, Aditya Acharya, and Philip Dasler. 2048 Without New Tiles Is Still Hard. In 8th International Conference on Fun with Algorithms (FUN 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 49, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{abdelkader_et_al:LIPIcs.FUN.2016.1,
  author =	{Abdelkader, Ahmed and Acharya, Aditya and Dasler, Philip},
  title =	{{2048 Without New Tiles Is Still Hard}},
  booktitle =	{8th International Conference on Fun with Algorithms (FUN 2016)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-005-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{49},
  editor =	{Demaine, Erik D. and Grandoni, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2016.1},
  URN =		{urn:nbn:de:0030-drops-58858},
  doi =		{10.4230/LIPIcs.FUN.2016.1},
  annote =	{Keywords: Complexity of Games, 2048}
}
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