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Documents authored by Kramer, Peter

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.74
Drainability and Fillability of Polyominoes in Diverse Models of Global Control

Authors: Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Tilt models offer intuitive and clean definitions of complex systems in which particles are influenced by global control commands. Despite a wide range of applications, there has been almost no theoretical investigation into the associated issues of filling and draining geometric environments. This is partly because a globally controlled system (i.e., passive matter) exhibits highly complex behavior that cannot be locally restricted. Thus, there is a strong need for theoretical studies that investigate these models both (1) in terms of relative power to each other, and (2) from a complexity theory perspective. In this work, we provide (1) general tools for comparing and contrasting different models of global control, and (2) both complexity and algorithmic results on filling and draining.
Cite as

Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Drainability and Fillability of Polyominoes in Diverse Models of Global Control. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 74:1-74:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fekete_et_al:LIPIcs.ICALP.2025.74,
  author =	{Fekete, S\'{a}ndor P. and Kramer, Peter and Reinhardt, Jan-Marc and Rieck, Christian and Scheffer, Christian},
  title =	{{Drainability and Fillability of Polyominoes in Diverse Models of Global Control}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{74:1--74:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.74},
  URN =		{urn:nbn:de:0030-drops-234518},
  doi =		{10.4230/LIPIcs.ICALP.2025.74},
  annote =	{Keywords: Global control, full Tilt, single Tilt, Fillability, Drainability, Polyominoes, Complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.29
Coordinated Motion Planning: Multi-Agent Path Finding in a Densely Packed, Bounded Domain

Authors: Sándor P. Fekete, Ramin Kosfeld, Peter Kramer, Jonas Neutzner, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
We study Multi-Agent Path Finding for arrangements of labeled agents in the interior of a simply connected domain: Given a unique start and target position for each agent, the goal is to find a sequence of parallel, collision-free agent motions that minimizes the overall time (the makespan) until all agents have reached their respective targets. A natural case is that of a simply connected polygonal domain with axis-parallel boundaries and integer coordinates, i.e., a simple polyomino, which amounts to a simply connected union of lattice unit squares or cells. We focus on the particularly challenging setting of densely packed agents, i.e., one per cell, which strongly restricts the mobility of agents, and requires intricate coordination of motion. We provide a variety of novel results for this problem, including (1) a characterization of polyominoes in which a reconfiguration plan is guaranteed to exist; (2) a characterization of shape parameters that induce worst-case bounds on the makespan; (3) a suite of algorithms to achieve asymptotically worst-case optimal performance with respect to the achievable stretch for cases with severely limited maneuverability. This corresponds to bounding the ratio between obtained makespan and the lower bound provided by the max-min distance between the start and target position of any agent and our shape parameters. Our results extend findings by Demaine et al. [Erik D. Demaine et al., 2018; Erik D. Demaine et al., 2019] who investigated the problem for solid rectangular domains, and in the closely related field of Permutation Routing, as presented by Alpert et al. [H. Alpert et al., 2022] for convex pieces of grid graphs.
Cite as

Sándor P. Fekete, Ramin Kosfeld, Peter Kramer, Jonas Neutzner, Christian Rieck, and Christian Scheffer. Coordinated Motion Planning: Multi-Agent Path Finding in a Densely Packed, Bounded Domain. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fekete_et_al:LIPIcs.ISAAC.2024.29,
  author =	{Fekete, S\'{a}ndor P. and Kosfeld, Ramin and Kramer, Peter and Neutzner, Jonas and Rieck, Christian and Scheffer, Christian},
  title =	{{Coordinated Motion Planning: Multi-Agent Path Finding in a Densely Packed, Bounded Domain}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.29},
  URN =		{urn:nbn:de:0030-drops-221565},
  doi =		{10.4230/LIPIcs.ISAAC.2024.29},
  annote =	{Keywords: multi-agent path finding, coordinated motion planning, bounded stretch, makespan, swarm robotics, reconfigurability, parallel sorting}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.17
Efficiently Reconfiguring a Connected Swarm of Labeled Robots

Authors: Sándor P. Fekete, Peter Kramer, Christian Rieck, Christian Scheffer, and Arne Schmidt

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

Abstract
When considering motion planning for a swarm of n labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel, continuous, collision-free robot motions. The objective is to reach the new configuration in a minimum amount of time; an important constraint is to keep the swarm connected at all times. Problems of this type have been considered before, with recent notable results achieving constant stretch for not necessarily connected reconfiguration: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, the total duration of an overall schedule can be bounded to 𝒪(d), which is optimal up to constant factors. However, constant stretch could only be achieved if disconnected reconfiguration is allowed, or for scaled configurations (which arise by increasing all dimensions of a given object by the same multiplicative factor) of unlabeled robots. We resolve these major open problems by (1) establishing a lower bound of Ω(√n) for connected, labeled reconfiguration and, most importantly, by (2) proving that for scaled arrangements, constant stretch for connected reconfiguration can be achieved. In addition, we show that (3) it is NP-hard to decide whether a makespan of 2 can be achieved, while it is possible to check in polynomial time whether a makespan of 1 can be achieved.
Cite as

Sándor P. Fekete, Peter Kramer, Christian Rieck, Christian Scheffer, and Arne Schmidt. Efficiently Reconfiguring a Connected Swarm of Labeled Robots. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fekete_et_al:LIPIcs.ISAAC.2022.17,
  author =	{Fekete, S\'{a}ndor P. and Kramer, Peter and Rieck, Christian and Scheffer, Christian and Schmidt, Arne},
  title =	{{Efficiently Reconfiguring a Connected Swarm of Labeled Robots}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{17:1--17:15},
  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.2022.17},
  URN =		{urn:nbn:de:0030-drops-173028},
  doi =		{10.4230/LIPIcs.ISAAC.2022.17},
  annote =	{Keywords: Motion planning, parallel motion, bounded stretch, makespan, connectivity, swarm robotics}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2022.65
Space Ants: Episode II - Coordinating Connected Catoms (Media Exposition)

Authors: Julien Bourgeois, Sándor P. Fekete, Ramin Kosfeld, Peter Kramer, Benoît Piranda, Christian Rieck, and Christian Scheffer

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

Abstract
How can a set of identical mobile agents coordinate their motions to transform their arrangement from a given starting to a desired goal configuration? We consider this question in the context of actual physical devices called Catoms, which can perform reconfiguration, but need to maintain connectivity at all times to ensure communication and energy supply. We demonstrate and animate algorithmic results, in particular a proof of hardness, as well as an algorithm that guarantees constant stretch for certain classes of arrangements: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, then the total duration of our overall schedule is in 𝒪(d), which is optimal up to constant factors.
Cite as

Julien Bourgeois, Sándor P. Fekete, Ramin Kosfeld, Peter Kramer, Benoît Piranda, Christian Rieck, and Christian Scheffer. Space Ants: Episode II - Coordinating Connected Catoms (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 65:1-65:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bourgeois_et_al:LIPIcs.SoCG.2022.65,
  author =	{Bourgeois, Julien and Fekete, S\'{a}ndor P. and Kosfeld, Ramin and Kramer, Peter and Piranda, Beno\^{i}t and Rieck, Christian and Scheffer, Christian},
  title =	{{Space Ants: Episode II - Coordinating Connected Catoms}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{65:1--65:6},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.65},
  URN =		{urn:nbn:de:0030-drops-160732},
  doi =		{10.4230/LIPIcs.SoCG.2022.65},
  annote =	{Keywords: Motion planning, parallel motion, bounded stretch, scaled shape, makespan, connectivity, swarm robotics}
}
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