29 Search Results for "Kostitsyna, Irina"

Document
DOI: 10.4230/DagRep.13.2.183
Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091)

Authors: Aaron Becker, Sándor Fekete, Irina Kostitsyna, Matthew J. Patitz, Damien Woods, and Ioannis Chatzigiannakis

Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23091, "Algorithmic Foundations of Programmable Matter", a new and emerging field that combines theoretical work on algorithms with a wide spectrum of practical applications that reach all the way from small-scale embedded systems to cyber-physical structures at nano-scale. The aim of this seminar was to bring together researchers from computational geometry, distributed computing, DNA computing, and swarm robotics who have worked on programmable matter to inform one another about the newest developments in each area and to discuss future models, approaches, and directions for new research. Similar to the first two Dagstuhl Seminars on programmable matter (16271 and 18331), we did focus on some basic problems, but also considered new problems that were now within reach to be studied.
Cite as

Aaron Becker, Sándor Fekete, Irina Kostitsyna, Matthew J. Patitz, Damien Woods, and Ioannis Chatzigiannakis. Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091). In Dagstuhl Reports, Volume 13, Issue 2, pp. 183-198, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{becker_et_al:DagRep.13.2.183,
  author =	{Becker, Aaron and Fekete, S\'{a}ndor and Kostitsyna, Irina and Patitz, Matthew J. and Woods, Damien and Chatzigiannakis, Ioannis},
  title =	{{Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091)}},
  pages =	{183--198},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{2},
  editor =	{Becker, Aaron and Fekete, S\'{a}ndor and Kostitsyna, Irina and Patitz, Matthew J. and Woods, Damien and Chatzigiannakis, Ioannis},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.13.2.183},
  URN =		{urn:nbn:de:0030-drops-191848},
  doi =		{10.4230/DagRep.13.2.183},
  annote =	{Keywords: computational geometry, distributed algorithms, DNA computing, programmable matter, swarm robotics}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.27
Fast Reconfiguration for Programmable Matter

Authors: Irina Kostitsyna, Tom Peters, and Bettina Speckmann

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their actions can nevertheless result in the global change of the material’s physical properties and geometry. A fundamental algorithmic task for programmable matter is to achieve global shape reconfiguration by specifying local behavior of the particles. In this paper we describe a new approach for shape reconfiguration in the amoebot model. The amoebot model is a distributed model which significantly restricts memory, computing, and communication capacity of the individual particles. Thus the challenge lies in coordinating the actions of particles to produce the desired behavior of the global system. Our reconfiguration algorithm is the first algorithm that does not use a canonical intermediate configuration when transforming between arbitrary shapes. We introduce new geometric primitives for amoebots and show how to reconfigure particle systems, using these primitives, in a linear number of activation rounds in the worst case. In practice, our method exploits the geometry of the symmetric difference between input and output shape: it minimizes unnecessary disassembly and reassembly of the particle system when the symmetric difference between the initial and the target shapes is small. Furthermore, our reconfiguration algorithm moves the particles over as many parallel shortest paths as the problem instance allows.
Cite as

Irina Kostitsyna, Tom Peters, and Bettina Speckmann. Fast Reconfiguration for Programmable Matter. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kostitsyna_et_al:LIPIcs.DISC.2023.27,
  author =	{Kostitsyna, Irina and Peters, Tom and Speckmann, Bettina},
  title =	{{Fast Reconfiguration for Programmable Matter}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.27},
  URN =		{urn:nbn:de:0030-drops-191533},
  doi =		{10.4230/LIPIcs.DISC.2023.27},
  annote =	{Keywords: Programmable matter, amoebot model, shape reconfiguration}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.47
Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter

Authors: Irina Kostitsyna, Tom Peters, and Bettina Speckmann

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material that can change its physical properties and shape based on the outcome of computation and movement performed by the individual particles in a concurrent manner. We use geometric insights to develop a new type of shortest path tree for programmable matter systems. Our feather trees utilize geometry to allow particles and information to traverse the programmable matter structure via shortest paths even in the presence of multiple overlapping trees.
Cite as

Irina Kostitsyna, Tom Peters, and Bettina Speckmann. Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 47:1-47:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kostitsyna_et_al:LIPIcs.DISC.2022.47,
  author =	{Kostitsyna, Irina and Peters, Tom and Speckmann, Bettina},
  title =	{{Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{47:1--47:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.47},
  URN =		{urn:nbn:de:0030-drops-172386},
  doi =		{10.4230/LIPIcs.DISC.2022.47},
  annote =	{Keywords: Programmable matter, amoebot model, shape reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.DNA.28.9
Fault-Tolerant Shape Formation in the Amoebot Model

Authors: Irina Kostitsyna, Christian Scheideler, and Daniel Warner

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
The amoebot model is a distributed computing model of programmable matter. It envisions programmable matter as a collection of computational units called amoebots or particles that utilize local interactions to achieve tasks of coordination, movement and conformation. In the geometric amoebot model the particles operate on a hexagonal tessellation of the plane. Within this model, numerous problems such as leader election, shape formation or object coating have been studied. One area that has not received much attention so far, but is highly relevant for a practical implementation of programmable matter, is fault tolerance. The existing literature on that aspect allows particles to crash but assumes that crashed particles do not recover. We proposed a new model [Kostitsyna et al., 2022] in which a crash causes the memory of a particle to be reset and a crashed particle can detect that it has crashed and try to recover using its local information and communication capabilities. We present an algorithm that solves the hexagon shape formation problem in our model if a finite number of crashes occur and a designated leader particle does not fail. At the heart of our solution lies a fault-tolerant implementation of the spanning forest primitive, which, since other algorithms in the amoebot model also make use of it, is also of general interest.
Cite as

Irina Kostitsyna, Christian Scheideler, and Daniel Warner. Fault-Tolerant Shape Formation in the Amoebot Model. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kostitsyna_et_al:LIPIcs.DNA.28.9,
  author =	{Kostitsyna, Irina and Scheideler, Christian and Warner, Daniel},
  title =	{{Fault-Tolerant Shape Formation in the Amoebot Model}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{9:1--9:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.9},
  URN =		{urn:nbn:de:0030-drops-167949},
  doi =		{10.4230/LIPIcs.DNA.28.9},
  annote =	{Keywords: programmable matter, amoebot model, fault tolerance, shape formation}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.4
Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares

Authors: Hugo A. Akitaya, Erik D. Demaine, Matias Korman, Irina Kostitsyna, Irene Parada, Willem Sonke, Bettina Speckmann, Ryuhei Uehara, and Jules Wulms

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
Edge-connected configurations of square modules, which can reconfigure through so-called sliding moves, are a well-established theoretical model for modular robots in two dimensions. Dumitrescu and Pach [Graphs and Combinatorics, 2006] proved that it is always possible to reconfigure one edge-connected configuration of n squares into any other using at most O(n²) sliding moves, while keeping the configuration connected at all times. For certain pairs of configurations, reconfiguration may require Ω(n²) sliding moves. However, significantly fewer moves may be sufficient. We prove that it is NP-hard to minimize the number of sliding moves for a given pair of edge-connected configurations. On the positive side we present Gather&Compact, an input-sensitive in-place algorithm that requires only O( ̄P n) sliding moves to transform one configuration into the other, where ̄P is the maximum perimeter of the two bounding boxes. The squares move within the bounding boxes only, with the exception of at most one square at a time which may move through the positions adjacent to the bounding boxes. The O( ̄P n) bound never exceeds O(n²), and is optimal (up to constant factors) among all bounds parameterized by just n and ̄P. Our algorithm is built on the basic principle that well-connected components of modular robots can be transformed efficiently. Hence we iteratively increase the connectivity within a configuration, to finally arrive at a single solid xy-monotone component. We implemented Gather&Compact and compared it experimentally to the in-place modification by Moreno and Sacristán [EuroCG 2020] of the Dumitrescu and Pach algorithm (MSDP). Our experiments show that Gather&Compact consistently outperforms MSDP by a significant margin, on all types of square configurations.
Cite as

Hugo A. Akitaya, Erik D. Demaine, Matias Korman, Irina Kostitsyna, Irene Parada, Willem Sonke, Bettina Speckmann, Ryuhei Uehara, and Jules Wulms. Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{a.akitaya_et_al:LIPIcs.SWAT.2022.4,
  author =	{A. Akitaya, Hugo and Demaine, Erik D. and Korman, Matias and Kostitsyna, Irina and Parada, Irene and Sonke, Willem and Speckmann, Bettina and Uehara, Ryuhei and Wulms, Jules},
  title =	{{Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.4},
  URN =		{urn:nbn:de:0030-drops-161644},
  doi =		{10.4230/LIPIcs.SWAT.2022.4},
  annote =	{Keywords: Sliding cubes, Reconfiguration, Modular robots, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.12
Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds

Authors: Bahareh Banyassady, Mark de Berg, Karl Bringmann, Kevin Buchin, Henning Fernau, Dan Halperin, Irina Kostitsyna, Yoshio Okamoto, and Stijn Slot

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We consider the unlabeled motion-planning problem of m unit-disc robots moving in a simple polygonal workspace of n edges. The goal is to find a motion plan that moves the robots to a given set of m target positions. For the unlabeled variant, it does not matter which robot reaches which target position as long as all target positions are occupied in the end. If the workspace has narrow passages such that the robots cannot fit through them, then the free configuration space, representing all possible unobstructed positions of the robots, will consist of multiple connected components. Even if in each component of the free space the number of targets matches the number of start positions, the motion-planning problem does not always have a solution when the robots and their targets are positioned very densely. In this paper, we prove tight bounds on how much separation between start and target positions is necessary to always guarantee a solution. Moreover, we describe an algorithm that always finds a solution in time O(n log n + mn + m²) if the separation bounds are met. Specifically, we prove that the following separation is sufficient: any two start positions are at least distance 4 apart, any two target positions are at least distance 4 apart, and any pair of a start and a target positions is at least distance 3 apart. We further show that when the free space consists of a single connected component, the separation between start and target positions is not necessary.
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Bahareh Banyassady, Mark de Berg, Karl Bringmann, Kevin Buchin, Henning Fernau, Dan Halperin, Irina Kostitsyna, Yoshio Okamoto, and Stijn Slot. Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{banyassady_et_al:LIPIcs.SoCG.2022.12,
  author =	{Banyassady, Bahareh and de Berg, Mark and Bringmann, Karl and Buchin, Kevin and Fernau, Henning and Halperin, Dan and Kostitsyna, Irina and Okamoto, Yoshio and Slot, Stijn},
  title =	{{Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.12},
  URN =		{urn:nbn:de:0030-drops-160203},
  doi =		{10.4230/LIPIcs.SoCG.2022.12},
  annote =	{Keywords: motion planning, computational geometry, simple polygon}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2022.23
Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model

Authors: Irina Kostitsyna, Christian Scheideler, and Daniel Warner

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
The amoebot model is a distributed computing model of programmable matter. It envisions programmable matter as a collection of computational units called amoebots or particles that utilize local interactions to achieve tasks of coordination, movement and conformation. In the geometric amoebot model the particles operate on a hexagonal tessellation of the plane. Within this model, numerous problems such as leader election, shape formation or object coating have been studied. One area that has not received much attention so far, but is highly relevant for a practical implementation of programmable matter, is fault tolerance. The existing literature on that aspect allows particles to crash but assumes that crashed particles do not recover. We propose a new model in which a crash causes the memory of a particle to be reset and a crashed particle can detect that it has crashed and try to recover using its local information and communication capabilities. We propose an algorithm that solves the hexagon shape formation problem in our model if a finite number of crashes occur and a designated leader particle does not fail. At the heart of our solution lies a fault-tolerant implementation of the spanning forest primitive, which, since other algorithms in the amoebot model also make use of it, is also of general interest.
Cite as

Irina Kostitsyna, Christian Scheideler, and Daniel Warner. Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 23:1-23:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kostitsyna_et_al:LIPIcs.SAND.2022.23,
  author =	{Kostitsyna, Irina and Scheideler, Christian and Warner, Daniel},
  title =	{{Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{23:1--23:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.23},
  URN =		{urn:nbn:de:0030-drops-159656},
  doi =		{10.4230/LIPIcs.SAND.2022.23},
  annote =	{Keywords: Programmable matter, Geometric amoebot model, Fault tolerance, Shape formation}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.25
Dots & Boxes Is PSPACE-Complete

Authors: Kevin Buchin, Mart Hagedoorn, Irina Kostitsyna, and Max van Mulken

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Exactly 20 years ago at MFCS, Demaine posed the open problem whether the game of Dots & Boxes is PSPACE-complete. Dots & Boxes has been studied extensively, with for instance a chapter in Berlekamp et al. Winning Ways for Your Mathematical Plays, a whole book on the game The Dots and Boxes Game: Sophisticated Child’s Play by Berlekamp, and numerous articles in the Games of No Chance series. While known to be NP-hard, the question of its complexity remained open. We resolve this question, proving that the game is PSPACE-complete by a reduction from a game played on propositional formulas.
Cite as

Kevin Buchin, Mart Hagedoorn, Irina Kostitsyna, and Max van Mulken. Dots & Boxes Is PSPACE-Complete. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{buchin_et_al:LIPIcs.MFCS.2021.25,
  author =	{Buchin, Kevin and Hagedoorn, Mart and Kostitsyna, Irina and van Mulken, Max},
  title =	{{Dots \& Boxes Is PSPACE-Complete}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.25},
  URN =		{urn:nbn:de:0030-drops-144657},
  doi =		{10.4230/LIPIcs.MFCS.2021.25},
  annote =	{Keywords: Dots \& Boxes, PSPACE-complete, combinatorial game}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.5
Chasing Puppies: Mobile Beacon Routing on Closed Curves

Authors: Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others’ work on beacon-based routing. Consider a human and a puppy on a simple closed curve in the plane. The human can walk along the curve at bounded speed and change direction as desired. The puppy runs with unbounded speed along the curve as long as the Euclidean straight-line distance to the human is decreasing, so that it is always at a point on the curve where the distance is locally minimal. Assuming that the curve is smooth (with some mild genericity constraints) or a simple polygon, we prove that the human can always catch the puppy in finite time.
Cite as

Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta. Chasing Puppies: Mobile Beacon Routing on Closed Curves. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2021.5,
  author =	{Abrahamsen, Mikkel and Erickson, Jeff and Kostitsyna, Irina and L\"{o}ffler, Maarten and Miltzow, Tillmann and Urhausen, J\'{e}r\^{o}me and Vermeulen, Jordi and Viglietta, Giovanni},
  title =	{{Chasing Puppies: Mobile Beacon Routing on Closed Curves}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.5},
  URN =		{urn:nbn:de:0030-drops-138046},
  doi =		{10.4230/LIPIcs.SoCG.2021.5},
  annote =	{Keywords: Beacon routing, navigation, generic smooth curves, puppies}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.4
Minimum Scan Cover and Variants - Theory and Experiments

Authors: Kevin Buchin, Sándor P. Fekete, Alexander Hill, Linda Kleist, Irina Kostitsyna, Dominik Krupke, Roel Lambers, and Martijn Struijs

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. In order to scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex. Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this paper, we present polynomial-time algorithms for 1D instances of MSC-TE and MSC-BE, but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches, and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.
Cite as

Kevin Buchin, Sándor P. Fekete, Alexander Hill, Linda Kleist, Irina Kostitsyna, Dominik Krupke, Roel Lambers, and Martijn Struijs. Minimum Scan Cover and Variants - Theory and Experiments. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{buchin_et_al:LIPIcs.SEA.2021.4,
  author =	{Buchin, Kevin and Fekete, S\'{a}ndor P. and Hill, Alexander and Kleist, Linda and Kostitsyna, Irina and Krupke, Dominik and Lambers, Roel and Struijs, Martijn},
  title =	{{Minimum Scan Cover and Variants - Theory and Experiments}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.4},
  URN =		{urn:nbn:de:0030-drops-137765},
  doi =		{10.4230/LIPIcs.SEA.2021.4},
  annote =	{Keywords: Graph scanning, angular metric, makespan, energy, bottleneck, complexity, approximation, algorithm engineering, mixed-integer programming, constraint programming}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.15
Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard

Authors: Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, and Remco J. A. Surtel

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots of two different sizes. That is, within one class of robots, where a class is given by the robots' size, any robot can be moved to any of the corresponding target positions. We prove that the decision problem of whether there exists a schedule moving the robots to the target positions is PSPACE-hard.
Cite as

Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, and Remco J. A. Surtel. Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brocken_et_al:LIPIcs.FUN.2021.15,
  author =	{Brocken, Thomas and van der Heijden, G. Wessel and Kostitsyna, Irina and Lo-Wong, Lloyd E. and Surtel, Remco J. A.},
  title =	{{Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.15},
  URN =		{urn:nbn:de:0030-drops-127769},
  doi =		{10.4230/LIPIcs.FUN.2021.15},
  annote =	{Keywords: Disc-robot motion planning, algorithmic complexity, PSPACE-hard}
}
Document
DOI: 10.4230/LIPIcs.DNA.2020.11
Turning Machines

Authors: Irina Kostitsyna, Cai Wood, and Damien Woods

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We fully characterise the ability of Turning Machines to execute line rotations, and to do so efficiently: computing an almost-full line rotation of 5π/3 radians is possible, yet a full 2π rotation is impossible. We show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold arbitrarily large zig-zag-rastered squares and y-monotone shapes.
Cite as

Irina Kostitsyna, Cai Wood, and Damien Woods. Turning Machines. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kostitsyna_et_al:LIPIcs.DNA.2020.11,
  author =	{Kostitsyna, Irina and Wood, Cai and Woods, Damien},
  title =	{{Turning Machines}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.11},
  URN =		{urn:nbn:de:0030-drops-129649},
  doi =		{10.4230/LIPIcs.DNA.2020.11},
  annote =	{Keywords: model of computation, molecular robotics, self-assembly, nubot, reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.24
Geometric Secluded Paths and Planar Satisfiability

Authors: Kevin Buchin, Valentin Polishchuk, Leonid Sedov, and Roman Voronov

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

Abstract
We consider paths with low exposure to a 2D polygonal domain, i.e., paths which are seen as little as possible; we differentiate between integral exposure (when we care about how long the path sees every point of the domain) and 0/1 exposure (just counting whether a point is seen by the path or not). For the integral exposure, we give a PTAS for finding the minimum-exposure path between two given points in the domain; for the 0/1 version, we prove that in a simple polygon the shortest path has the minimum exposure, while in domains with holes the problem becomes NP-hard. We also highlight connections of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.
Cite as

Kevin Buchin, Valentin Polishchuk, Leonid Sedov, and Roman Voronov. Geometric Secluded Paths and Planar Satisfiability. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{buchin_et_al:LIPIcs.SoCG.2020.24,
  author =	{Buchin, Kevin and Polishchuk, Valentin and Sedov, Leonid and Voronov, Roman},
  title =	{{Geometric Secluded Paths and Planar Satisfiability}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{24:1--24:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.24},
  URN =		{urn:nbn:de:0030-drops-121827},
  doi =		{10.4230/LIPIcs.SoCG.2020.24},
  annote =	{Keywords: Visibility, Route planning, Security/privacy, Planar satisfiability}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.43
Minimum Scan Cover with Angular Transition Costs

Authors: Sándor P. Fekete, Linda Kleist, and Dominik Krupke

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

Abstract
We provide a comprehensive study of a natural geometric optimization problem motivated by questions in the context of satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs (msc), we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. In order to scan their edge, two vertices need to face each other; changing the heading of a vertex takes some time proportional to the corresponding turn angle. Our goal is to minimize the time until all scans are completed, i.e., to compute a schedule of minimum makespan. We show that msc is closely related to both graph coloring and the minimum (directed and undirected) cut cover problem; in particular, we show that the minimum scan time for instances in 1D and 2D lies in Θ(log χ(G)), while for 3D the minimum scan time is not upper bounded by χ(G). We use this relationship to prove that the existence of a constant-factor approximation implies P=NP, even for one-dimensional instances. In 2D, we show that it is NP-hard to approximate a minimum scan cover within less than a factor of 3/2, even for bipartite graphs; conversely, we present a 9/2-approximation algorithm for this scenario. Generally, we give an O(c)-approximation for k-colored graphs with k ≤ χ(G)^c. For general metric cost functions, we provide approximation algorithms whose performance guarantee depend on the arboricity of the graph.
Cite as

Sándor P. Fekete, Linda Kleist, and Dominik Krupke. Minimum Scan Cover with Angular Transition Costs. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 43:1-43:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fekete_et_al:LIPIcs.SoCG.2020.43,
  author =	{Fekete, S\'{a}ndor P. and Kleist, Linda and Krupke, Dominik},
  title =	{{Minimum Scan Cover with Angular Transition Costs}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{43:1--43:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.43},
  URN =		{urn:nbn:de:0030-drops-122014},
  doi =		{10.4230/LIPIcs.SoCG.2020.43},
  annote =	{Keywords: Graph scanning, graph coloring, angular metric, complexity, approximation, scheduling}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2020.79
Dots & Polygons (Media Exposition)

Authors: Kevin Buchin, Mart Hagedoorn, Irina Kostitsyna, Max van Mulken, Jolan Rensen, and Leo van Schooten

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

Abstract
We present a new game, Dots & Polygons, played on a planar point set. We prove that its NP-hard and discuss strategies for the case when the point set is in convex position.
Cite as

Kevin Buchin, Mart Hagedoorn, Irina Kostitsyna, Max van Mulken, Jolan Rensen, and Leo van Schooten. Dots & Polygons (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 79:1-79:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{buchin_et_al:LIPIcs.SoCG.2020.79,
  author =	{Buchin, Kevin and Hagedoorn, Mart and Kostitsyna, Irina and van Mulken, Max and Rensen, Jolan and van Schooten, Leo},
  title =	{{Dots \& Polygons}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{79:1--79:4},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.79},
  URN =		{urn:nbn:de:0030-drops-122371},
  doi =		{10.4230/LIPIcs.SoCG.2020.79},
  annote =	{Keywords: Dots \& Boxes, NP-hard, game, cycle packing}
}
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