10 Search Results for "Damian, Mirela"

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.22
Minimum Partition of Polygons Under Width and Cut Constraints

Authors: Jaehoon Chung, Kazuo Iwama, Chung-Shou Liao, and Hee-Kap Ahn

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width constraint for a set of unit vectors if the length of the orthogonal projection of the polygon on a line parallel to a vector in the set is at most one. We analyze structural properties of the minimum partition numbers, focusing on monotonicity under polygon containment. We show that the minimum partition number of a simple polygon is at least that of any subpolygon, provided that the subpolygon satisfies a certain orientation-wise convexity with respect to the polygon. As a consequence, we prove a partition analogue of the Bang’s conjecture about coverings of convex regions in the plane: for any partition of a convex body in the plane, the sum of relative widths of all parts is at least one. For any convex polygon, there exists a direction along which an optimal partition is achieved by parallel cuts. Given such a direction, an optimal partition can be computed in linear time.
Cite as

Jaehoon Chung, Kazuo Iwama, Chung-Shou Liao, and Hee-Kap Ahn. Minimum Partition of Polygons Under Width and Cut Constraints. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chung_et_al:LIPIcs.ISAAC.2025.22,
  author =	{Chung, Jaehoon and Iwama, Kazuo and Liao, Chung-Shou and Ahn, Hee-Kap},
  title =	{{Minimum Partition of Polygons Under Width and Cut Constraints}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.22},
  URN =		{urn:nbn:de:0030-drops-249302},
  doi =		{10.4230/LIPIcs.ISAAC.2025.22},
  annote =	{Keywords: Polygon partitioning, Width constraints, Plank problem}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.5
Constrained Flips in Plane Spanning Trees

Authors: Oswin Aichholzer, Joseph Dorfer, and Birgit Vogtenhuber

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A flip in a plane spanning tree T is the operation of removing one edge from T and adding another edge such that the resulting structure is again a plane spanning tree. For trees on a set of points in convex position we study two classic types of constrained flips: (1) Compatible flips are flips in which the removed and inserted edge do not cross each other. We relevantly improve the previous upper bound of 2n-O(√n) on the diameter of the compatible flip graph to (5n/3)-O(1), by this matching the upper bound for unrestricted flips by Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber [SODA 2025] up to an additive constant of 1. We further show that no shortest compatible flip sequence removes an edge that is already in its target position. Using this so-called happy edge property, we derive a fixed-parameter tractable algorithm to compute the shortest compatible flip sequence between two given trees. (2) Rotations are flips in which the removed and inserted edge share a common vertex. Besides showing that the happy edge property does not hold for rotations, we improve the previous upper bound of 2n-O(1) for the diameter of the rotation graph to (7n/4)-O(1).
Cite as

Oswin Aichholzer, Joseph Dorfer, and Birgit Vogtenhuber. Constrained Flips in Plane Spanning Trees. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.5,
  author =	{Aichholzer, Oswin and Dorfer, Joseph and Vogtenhuber, Birgit},
  title =	{{Constrained Flips in Plane Spanning Trees}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.5},
  URN =		{urn:nbn:de:0030-drops-249913},
  doi =		{10.4230/LIPIcs.GD.2025.5},
  annote =	{Keywords: Non-crossing spanning trees, Flip Graphs, Diameter, Complexity, Happy edges}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.47
Reconfigurations of Plane Caterpillars and Paths (Poster Abstract)

Authors: Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Let S be a point set in the plane, and let 𝒫(S) and 𝒞(S) be the sets of all plane spanning paths and caterpillars on S. We study reconfiguration operations on 𝒫(S) and 𝒞(S). In particular, we prove that all of the commonly studied reconfigurations on plane spanning trees still yield connected reconfiguration graphs for caterpillars when S is in convex position. If S is in general position, we show that the rotation, compatible flip and flip graphs of 𝒞(S) are connected while the slide graph is sometimes disconnected, but always has a component of size 1/4(3ⁿ-1). We then study sizes of connected components in reconfiguration graphs of plane spanning paths. In this direction, we show that no component of size at most 7 can exist in the flip graph on 𝒫(S).
Cite as

Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić. Reconfigurations of Plane Caterpillars and Paths (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 47:1-47:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antic_et_al:LIPIcs.GD.2025.47,
  author =	{Anti\'{c}, Todor and Gamboa Quintero, Guillermo and Gli\v{s}i\'{c}, Jelena},
  title =	{{Reconfigurations of Plane Caterpillars and Paths}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{47:1--47:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.47},
  URN =		{urn:nbn:de:0030-drops-250337},
  doi =		{10.4230/LIPIcs.GD.2025.47},
  annote =	{Keywords: reconfiguration graph, caterpillar, path, geometric graph}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.28
Sliding Squares in Parallel

Authors: Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given n square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of sliding moves to transform it into a desired goal configuration, maintaining connectivity of the configuration at all times. Recent work has aimed at minimizing the total number of moves, resulting in fully sequential schedules that can perform reconfiguration in 𝒪(n²) moves, or 𝒪(nP) for arrangements of bounding box perimeter size P. We provide first results in the sliding square model that exploit parallel motion, performing reconfiguration in worst-case optimal makespan of 𝒪(P). We also provide tight bounds on the complexity of the problem by showing that even deciding the possibility of reconfiguration within makespan 1 is NP-complete in the unlabeled case. In the labeled variant, we note that deciding the same for makespan 2 is NP-complete, while makespan 1 is straightforward.
Cite as

Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner. Sliding Squares in Parallel. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{a.akitaya_et_al:LIPIcs.ESA.2025.28,
  author =	{A. Akitaya, Hugo and Fekete, S\'{a}ndor P. and Kramer, Peter and Molaei, Saba and Rieck, Christian and Stock, Frederick and Wallner, Tobias},
  title =	{{Sliding Squares in Parallel}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.28},
  URN =		{urn:nbn:de:0030-drops-244961},
  doi =		{10.4230/LIPIcs.ESA.2025.28},
  annote =	{Keywords: Sliding squares, parallel motion, reconfigurability, motion planning, multi-agent path finding, makespan, swarm robotics, computational geometry}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.9
Online Routing in Directed Yao₄^∞ Graphs

Authors: Prosenjit Bose, Jean-Lou De Carufel, and John Stuart

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

Abstract
The x⃑{Yao₄^∞} and x⃑{Yao₄} graphs are two families of directed geometric graphs whose vertices are points in the plane, and each vertex has up to four outgoing edges. Consider a horizontal and a vertical line through each vertex v, defining four quadrants around v. Then v has an outgoing edge to the closest vertex in each of its four quadrants. When the distance is measured using the Euclidean norm, the resulting graph is the x⃑{Yao₄} graph, whereas with the L_∞-norm, we obtain the x⃑{Yao^{∞}₄} graph, which is a sub-graph of the well-known L_∞-Delaunay graph. In this paper, we provide a local routing algorithm with routing ratio at most 85.22 for x⃑{Yao^{∞}₄} graphs. Prior to this work, no constant spanning or routing ratios for x⃑{Yao₄^∞} graphs were previously known. Now, x⃑{Yao₄^∞} graphs are the sparsest family of directed planar graphs supporting a competitive local routing strategy. Furthermore, we show that no local routing algorithm for x⃑{Yao₄^∞} graphs can have a routing ratio lower than 7+√2≈ 8.41. Moreover, we prove that the spanning ratio is at least 5+√2≈ 6.41 in the worst case. The techniques we develop in this paper also allow us to prove lower bounds of 7-√3+√{5-2√3}≈ 6.51 and 7+√2 for the spanning and routing ratios of x⃑{Yao₄}, respectively.
Cite as

Prosenjit Bose, Jean-Lou De Carufel, and John Stuart. Online Routing in Directed Yao₄^∞ Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bose_et_al:LIPIcs.WADS.2025.9,
  author =	{Bose, Prosenjit and De Carufel, Jean-Lou and Stuart, John},
  title =	{{Online Routing in Directed Yao₄^∞ Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{9:1--9:22},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-242404},
  doi =		{10.4230/LIPIcs.WADS.2025.9},
  annote =	{Keywords: Geometric Spanners, Yao Graphs, Local Routing Algorithms}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2025.85
Finding Shortest Reconfiguration Sequences for Modular Robots (Media Exposition)

Authors: UML Modular Robotics Group, Hugo A. Akitaya, Andrew Clements, Sam Downey, Jonathan Eisenbies, Soham Samanta, Gabriel Shahrouzi, and Frederick Stock

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

Abstract
This paper introduces a set of tools built to help researchers design algorithms for modular robots. These tools can brute force solutions to specific reconfigurations, visualize movements of modular robots, and can be used to design specific configurations of robots. Multiple models of modular robots are supported, and can be added by users.
Cite as

UML Modular Robotics Group, Hugo A. Akitaya, Andrew Clements, Sam Downey, Jonathan Eisenbies, Soham Samanta, Gabriel Shahrouzi, and Frederick Stock. Finding Shortest Reconfiguration Sequences for Modular Robots (Media Exposition). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 85:1-85:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{umlmodularroboticsgroup_et_al:LIPIcs.SoCG.2025.85,
  author =	{UML Modular Robotics Group and A. Akitaya, Hugo and Clements, Andrew and Downey, Sam and Eisenbies, Jonathan and Samanta, Soham and Shahrouzi, Gabriel and Stock, Frederick},
  title =	{{Finding Shortest Reconfiguration Sequences for Modular Robots}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{85:1--85:5},
  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.2025.85},
  URN =		{urn:nbn:de:0030-drops-232371},
  doi =		{10.4230/LIPIcs.SoCG.2025.85},
  annote =	{Keywords: modular reconfigurable robots, sliding cube model, reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.8
Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees

Authors: Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang

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

Abstract
We show that the flip chain for non-crossing spanning trees of n+1 points in convex position mixes in time O(n⁸log n). We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wilson’s lattice path chain (Wilson 2004).
Cite as

Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang. Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.SoCG.2025.8,
  author =	{Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Jerrum, Mark and Wang, Jiaheng},
  title =	{{Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{8:1--8:18},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-231607},
  doi =		{10.4230/LIPIcs.SoCG.2025.8},
  annote =	{Keywords: non-crossing spanning trees, Markov chain, mixing time}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.51
Parameterized Geometric Graph Modification with Disk Scaling

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
The parameterized analysis of graph modification problems represents the most extensively studied area within Parameterized Complexity. Given a graph G and an integer k ∈ ℕ as input, the goal is to determine whether we can perform at most k operations on G to transform it into a graph belonging to a specified graph class ℱ. Typical operations are combinatorial and include vertex deletions and edge deletions, insertions, and contractions. However, in many real-world scenarios, when the input graph is constrained to be a geometric intersection graph, the modification of the graph is influenced by changes in the geometric properties of the underlying objects themselves, rather than by combinatorial modifications. It raises the question of whether vertex deletions or adjacency modifications are necessarily the most appropriate modification operations for studying modifications of geometric graphs. We propose the study of the disk intersection graph modification through the scaling of disks. This operation is typical in the realm of topology control but has not yet been explored in the context of Parameterized Complexity. We design parameterized algorithms and kernels for modifying to the most basic graph classes: edgeless, connected, and acyclic. Our technical contributions encompass a novel combination of linear programming, branching, and kernelization techniques, along with a fresh application of bidimensionality theory to analyze the area covered by disks, which may have broader applicability.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Parameterized Geometric Graph Modification with Disk Scaling. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ITCS.2025.51,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Parameterized Geometric Graph Modification with Disk Scaling}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{51:1--51:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-226795},
  doi =		{10.4230/LIPIcs.ITCS.2025.51},
  annote =	{Keywords: parameterized algorithms, kernelization, spreading points, distant representatives, unit disk packing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.3
Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

Authors: Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmović, Robin Flatland, Matias Korman, Belen Palop, Irene Parada, André van Renssen, and Vera Sacristán

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers") suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses O(n^2) pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive "sliding" moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models.
Cite as

Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmović, Robin Flatland, Matias Korman, Belen Palop, Irene Parada, André van Renssen, and Vera Sacristán. Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{akitaya_et_al:LIPIcs.ESA.2019.3,
  author =	{Akitaya, Hugo A. and Arkin, Esther M. and Damian, Mirela and Demaine, Erik D. and Dujmovi\'{c}, Vida and Flatland, Robin and Korman, Matias and Palop, Belen and Parada, Irene and van Renssen, Andr\'{e} and Sacrist\'{a}n, Vera},
  title =	{{Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.3},
  URN =		{urn:nbn:de:0030-drops-111247},
  doi =		{10.4230/LIPIcs.ESA.2019.3},
  annote =	{Keywords: Reconfiguration, geometric algorithm, pivoting squares, modular robots}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1345
Connecting Polygonizations via Stretches and Twangs

Authors: Mirela Damian, Robin Flatland, Joseph O'Rourke, and Suneeta Ramaswani

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We show that the space of polygonizations of a fixed planar point set $S$ of $n$ points is connected by $O(n^2)$ ``moves'' between simple polygons. Each move is composed of a sequence of atomic moves called ``stretches'' and ``twangs''. These atomic moves walk between weakly simple ``polygonal wraps'' of $S$. These moves show promise to serve as a basis for generating random polygons.
Cite as

Mirela Damian, Robin Flatland, Joseph O'Rourke, and Suneeta Ramaswani. Connecting Polygonizations via Stretches and Twangs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 217-228, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{damian_et_al:LIPIcs.STACS.2008.1345,
  author =	{Damian, Mirela and Flatland, Robin and O'Rourke, Joseph and Ramaswani, Suneeta},
  title =	{{Connecting Polygonizations via Stretches and Twangs}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{217--228},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1345},
  URN =		{urn:nbn:de:0030-drops-13457},
  doi =		{10.4230/LIPIcs.STACS.2008.1345},
  annote =	{Keywords: Polygons, polygonization, random polygons, connected configuration space}
}
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