4 Search Results for "Solovey, Kiril"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.43
Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs

Authors: Tsuri Farhana, Omrit Filtser, and Shalev Goldshtein

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We study unlabeled multi-robot motion planning for unit-disk robots in a polygonal environment. Although the problem is hard in general, polynomial-time solutions exist under appropriate separation assumptions on start and target positions. Solovey et al. (RSS'15) provide a near-optimal solution assuming that start/target positions must have pairwise distance at least 4, and at least √5≈2.236 from obstacles. This raises the question of whether polynomial-time algorithms can be obtained in even more densely packed environments. In this paper we present a generalized algorithm that achieve different trade-offs on the robots-separation and obstacles-separation bounds, all significantly improving upon the state of the art. Specifically, we obtain polynomial-time constant-approximation algorithms to minimize the total path length when (i) the robots-separation is 2 2/3 and the obstacles-separation is 1 2/3, or (ii) the robots-separation is ≈3.291 and the obstacles-separation ≈1.354. Additionally, we introduce a different strategy yielding a polynomial-time solution when the robots-separation is only 2, and the obstacles-separation is 3. Finally, we show that without any robots-separation assumption, obstacles-separation of at least 1.5 may be necessary for a solution to exist.
Cite as

Tsuri Farhana, Omrit Filtser, and Shalev Goldshtein. Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{farhana_et_al:LIPIcs.SoCG.2026.43,
  author =	{Farhana, Tsuri and Filtser, Omrit and Goldshtein, Shalev},
  title =	{{Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.43},
  URN =		{urn:nbn:de:0030-drops-258495},
  doi =		{10.4230/LIPIcs.SoCG.2026.43},
  annote =	{Keywords: multi-robot motion planning}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.5
Optimal Motion Planning for Two Square Robots in a Rectilinear Environment

Authors: Pankaj K. Agarwal, Mark de Berg, Benjamin Holmgren, Alex Steiger, and Martijn Struijs

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Let W ⊂ ℝ² be a rectilinear polygonal environment (that is, a rectilinear polygon potentially with holes) with a total of n vertices, and let A,B be two robots, each modeled as an axis-aligned unit square, that can move rectilinearly inside W. The goal is to compute an optimal collision-free motion plan π for A and B between a given pair of source and target configurations. We study two variants of this problem and obtain the following results. - Min-Sum: Here the goal is to compute a motion plan that minimizes the sum of the lengths of the paths of the robots. We present an O(n⁴log n)-time algorithm for computing an optimal solution to the min-sum problem. This is the first polynomial-time algorithm to compute an optimal, collision-free motion of two robots amid obstacles in a planar polygonal environment. - Min-Makespan: Here the robots can move with at most unit speed, and the goal is to compute a motion plan that minimizes the maximum time taken by a robot to reach its target location. We prove that the min-makespan variant is NP-hard.
Cite as

Pankaj K. Agarwal, Mark de Berg, Benjamin Holmgren, Alex Steiger, and Martijn Struijs. Optimal Motion Planning for Two Square Robots in a Rectilinear Environment. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2025.5,
  author =	{Agarwal, Pankaj K. and de Berg, Mark and Holmgren, Benjamin and Steiger, Alex and Struijs, Martijn},
  title =	{{Optimal Motion Planning for Two Square Robots in a Rectilinear Environment}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.5},
  URN =		{urn:nbn:de:0030-drops-231577},
  doi =		{10.4230/LIPIcs.SoCG.2025.5},
  annote =	{Keywords: Computational geometry, motion planning, multiple robots, rectilinear paths}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.1
Reconfiguration of Unit Squares and Disks: PSPACE-Hardness in Simple Settings

Authors: Mikkel Abrahamsen, Kevin Buchin, Maike Buchin, Linda Kleist, Maarten Löffler, Lena Schlipf, André Schulz, and Jack Stade

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study well-known reconfiguration problems. Given a start and a target configuration of geometric objects in a polygon, we wonder whether we can move the objects from the start configuration to the target configuration while avoiding collisions between the objects and staying within the polygon. Problems of this type have been considered since the early 80s by roboticists and computational geometers. In this paper, we study some of the simplest possible variants where the objects are labeled or unlabeled unit squares or unit disks. In unlabeled reconfiguration, the objects are identical, so that any object is allowed to end at any of the targets positions. In the labeled variant, each object has a designated target position. The results for the labeled variants are direct consequences from our insights on the unlabeled versions. We show that it is PSPACE-hard to decide whether there exists a reconfiguration of (unlabeled/labeled) unit squares even in a simple polygon. Previously, it was only known to be PSPACE-hard in a polygon with holes for both the unlabeled and labeled version [Solovey and Halperin, Int. J. Robotics Res. 2016]. Our proof is based on a result of independent interest, namely that reconfiguration between two satisfying assignments of a formula of Monotone-Planar-3-Sat is also PSPACE-complete. The reduction from reconfiguration of Monotone-Planar-3-Sat to reconfiguration of unit squares extends techniques recently developed to show NP-hardness of packing unit squares in a simple polygon [Abrahamsen and Stade, FOCS 2024]. We also show PSPACE-hardness of reconfiguration of (unlabeled/labeled) unit disks in a polygon with holes. Previously, it was known that unlabeled reconfiguration of disks of two different sizes was PSPACE-hard [Brocken, van der Heijden, Kostitsyna, Lo-Wong and Surtel, FUN 2021].
Cite as

Mikkel Abrahamsen, Kevin Buchin, Maike Buchin, Linda Kleist, Maarten Löffler, Lena Schlipf, André Schulz, and Jack Stade. Reconfiguration of Unit Squares and Disks: PSPACE-Hardness in Simple Settings. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2025.1,
  author =	{Abrahamsen, Mikkel and Buchin, Kevin and Buchin, Maike and Kleist, Linda and L\"{o}ffler, Maarten and Schlipf, Lena and Schulz, Andr\'{e} and Stade, Jack},
  title =	{{Reconfiguration of Unit Squares and Disks: PSPACE-Hardness in Simple Settings}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.1},
  URN =		{urn:nbn:de:0030-drops-231539},
  doi =		{10.4230/LIPIcs.SoCG.2025.1},
  annote =	{Keywords: reconfiguration, unit square, unit disk, unlabeled, labeled, simple polygon, polygon}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.76
Sampling-Based Bottleneck Pathfinding with Applications to Fréchet Matching

Authors: Kiril Solovey and Dan Halperin

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We describe a general probabilistic framework to address a variety of Fréchet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in d-dimensional Euclidean space between given start and goal points, namely paths that minimize the maximal value over a continuous cost map. We present an efficient and simple sampling-based framework for this problem, which is inspired by, and draws ideas from, techniques for robot motion planning. We extend the framework to handle not only standard bottleneck pathfinding, but also the more demanding case, where the path needs to be monotone in all dimensions. Finally, we provide experimental results of the framework on several types of problems.
Cite as

Kiril Solovey and Dan Halperin. Sampling-Based Bottleneck Pathfinding with Applications to Fréchet Matching. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 76:1-76:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{solovey_et_al:LIPIcs.ESA.2016.76,
  author =	{Solovey, Kiril and Halperin, Dan},
  title =	{{Sampling-Based Bottleneck Pathfinding with Applications to Fr\'{e}chet Matching}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{76:1--76:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.76},
  URN =		{urn:nbn:de:0030-drops-64179},
  doi =		{10.4230/LIPIcs.ESA.2016.76},
  annote =	{Keywords: Computational geometry, Fr\'{e}chet distances, sampling-based algorithms, random geometric graphs, bottleneck pathfinding}
}
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