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Documents authored by Taylor, Erin

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.2
Probabilistic Metric Embedding via Metric Labeling

Authors: Kamesh Munagala, Govind S. Sankar, and Erin Taylor

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We consider probabilistic embedding of metric spaces into ultra-metrics (or equivalently to a constant factor, into hierarchically separated trees) to minimize the expected distortion of any pairwise distance. Such embeddings have been widely used in network design and online algorithms. Our main result is a polynomial time algorithm that approximates the optimal distortion on any instance to within a constant factor. We achieve this via a novel LP formulation that reduces this problem to a probabilistic version of uniform metric labeling.
Cite as

Kamesh Munagala, Govind S. Sankar, and Erin Taylor. Probabilistic Metric Embedding via Metric Labeling. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{munagala_et_al:LIPIcs.APPROX/RANDOM.2023.2,
  author =	{Munagala, Kamesh and Sankar, Govind S. and Taylor, Erin},
  title =	{{Probabilistic Metric Embedding via Metric Labeling}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.2},
  URN =		{urn:nbn:de:0030-drops-188279},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.2},
  annote =	{Keywords: Metric Embedding, Approximation Algorithms, Ultrametrics}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.35
Multi-Robot Motion Planning for Unit Discs with Revolving Areas

Authors: Pankaj K. Agarwal, Tzvika Geft, Dan Halperin, and Erin Taylor

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study the problem of motion planning for a collection of n labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is contained in a radius 2 disc lying in the free space, not necessarily concentric with the start or final position, which is free from other start or final positions. This assumption allows a weakly-monotone motion plan, in which robots move according to an ordering as follows: during the turn of a robot R in the ordering, it moves fully from its start to final position, while other robots do not leave their revolving areas. As R passes through a revolving area, a robot R' that is inside this area may move within the revolving area to avoid a collision. Notwithstanding the existence of a motion plan, we show that minimizing the total traveled distance in this setting, specifically even when the motion plan is restricted to be weakly-monotone, is APX-hard, ruling out any polynomial-time (1+ε)-approximation algorithm. On the positive side, we present the first constant-factor approximation algorithm for computing a feasible weakly-monotone motion plan. The total distance traveled by the robots is within an O(1) factor of that of the optimal motion plan, which need not be weakly monotone. Our algorithm extends to an online setting in which the polygonal environment is fixed but the initial and final positions of robots are specified in an online manner. Finally, we observe that the overhead in the overall cost that we add while editing the paths to avoid robot-robot collision can vary significantly depending on the ordering we chose. Finding the best ordering in this respect is known to be NP-hard, and we provide a polynomial time O(log n log log n)-approximation algorithm for this problem.
Cite as

Pankaj K. Agarwal, Tzvika Geft, Dan Halperin, and Erin Taylor. Multi-Robot Motion Planning for Unit Discs with Revolving Areas. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{agarwal_et_al:LIPIcs.ISAAC.2022.35,
  author =	{Agarwal, Pankaj K. and Geft, Tzvika and Halperin, Dan and Taylor, Erin},
  title =	{{Multi-Robot Motion Planning for Unit Discs with Revolving Areas}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.35},
  URN =		{urn:nbn:de:0030-drops-173204},
  doi =		{10.4230/LIPIcs.ISAAC.2022.35},
  annote =	{Keywords: motion planning, optimal motion planning, approximation, complexity, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.8
Clustering Under Perturbation Stability in Near-Linear Time

Authors: Pankaj K. Agarwal, Hsien-Chih Chang, Kamesh Munagala, Erin Taylor, and Emo Welzl

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is α-stable if the underlying optimal clustering continues to remain optimal even when all pairwise distances are arbitrarily perturbed by a factor of at most α. Our main contribution is in presenting efficient exact algorithms for α-stable clustering instances whose running times depend near-linearly on the size of the data set when α ≥ 2 + √3. For k-center and k-means problems, our algorithms also achieve polynomial dependence on the number of clusters, k, when α ≥ 2 + √3 + ε for any constant ε > 0 in any fixed dimension. For k-median, our algorithms have polynomial dependence on k for α > 5 in any fixed dimension; and for α ≥ 2 + √3 in two dimensions. Our algorithms are simple, and only require applying techniques such as local search or dynamic programming to a suitably modified metric space, combined with careful choice of data structures.
Cite as

Pankaj K. Agarwal, Hsien-Chih Chang, Kamesh Munagala, Erin Taylor, and Emo Welzl. Clustering Under Perturbation Stability in Near-Linear Time. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agarwal_et_al:LIPIcs.FSTTCS.2020.8,
  author =	{Agarwal, Pankaj K. and Chang, Hsien-Chih and Munagala, Kamesh and Taylor, Erin and Welzl, Emo},
  title =	{{Clustering Under Perturbation Stability in Near-Linear Time}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.8},
  URN =		{urn:nbn:de:0030-drops-132492},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.8},
  annote =	{Keywords: clustering, stability, local search, dynamic programming, coreset, polyhedral metric, trapezoid decomposition, range query}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.58
k-Median Clustering Under Discrete Fréchet and Hausdorff Distances

Authors: Abhinandan Nath and Erin Taylor

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We give the first near-linear time (1+ε)-approximation algorithm for k-median clustering of polygonal trajectories under the discrete Fréchet distance, and the first polynomial time (1+ε)-approximation algorithm for k-median clustering of finite point sets under the Hausdorff distance, provided the cluster centers, ambient dimension, and k are bounded by a constant. The main technique is a general framework for solving clustering problems where the cluster centers are restricted to come from a simpler metric space. We precisely characterize conditions on the simpler metric space of the cluster centers that allow faster (1+ε)-approximations for the k-median problem. We also show that the k-median problem under Hausdorff distance is NP-Hard.
Cite as

Abhinandan Nath and Erin Taylor. k-Median Clustering Under Discrete Fréchet and Hausdorff Distances. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nath_et_al:LIPIcs.SoCG.2020.58,
  author =	{Nath, Abhinandan and Taylor, Erin},
  title =	{{k-Median Clustering Under Discrete Fr\'{e}chet and Hausdorff Distances}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.58},
  URN =		{urn:nbn:de:0030-drops-122161},
  doi =		{10.4230/LIPIcs.SoCG.2020.58},
  annote =	{Keywords: Clustering, k-median, trajectories, point sets, discrete Fr\'{e}chet distance, Hausdorff distance}
}
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