20 Search Results for "Kling, Peter"

Document
DOI: 10.4230/LIPIcs.STACS.2026.71
Broadcast in Almost Mixing Time

Authors: Anton Paramonov and Roger Wattenhofer

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the problem of broadcasting multiple messages in the CONGEST model. In this problem, a dedicated source node s possesses a set M of messages with every message of size O(log n) where n is the total number of nodes. The objective is to ensure that every node in the network learns all messages in M. The execution of an algorithm progresses in rounds, and we focus on optimizing the round complexity of broadcasting multiple messages. Our primary contribution is a randomized algorithm for networks with expander topology. The algorithm succeeds with high probability and achieves a round complexity that is optimal up to a factor of the network’s mixing time and polylogarithmic terms. It leverages a multi-COBRA primitive, which uses multiple branching random walks running in parallel. A crucial aspect of our method is the use of these branching random walks to construct an optimal (up to a polylogarithmic factor) tree packing of a random graph, which is then used for efficient broadcasting. We also prove the problem to be NP-hard in a centralized setting and provide insights into why lower bounds that can be matched in expanders, namely graph diameter and |M|/minCut, cannot be tight in general graphs.
Cite as

Anton Paramonov and Roger Wattenhofer. Broadcast in Almost Mixing Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 71:1-71:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{paramonov_et_al:LIPIcs.STACS.2026.71,
  author =	{Paramonov, Anton and Wattenhofer, Roger},
  title =	{{Broadcast in Almost Mixing Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{71:1--71:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.71},
  URN =		{urn:nbn:de:0030-drops-255603},
  doi =		{10.4230/LIPIcs.STACS.2026.71},
  annote =	{Keywords: Distributed algorithms, Expander Graphs, Random graphs, Broadcast, Branching random walks, Tree packing, CONGEST model}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.36
Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

Authors: Yi-Jun Chang, Lyuting Chen, and Haoran Zhou

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. They showed that in 2-edge-connected networks, any distributed algorithm can be simulated in the content-oblivious model, provided that a unique leader is designated a priori. Subsequent works of Frei, Gelles, Ghazy, and Nolin (DISC 2024) and Chalopin et al. (DISC 2025) developed content-oblivious leader election algorithms, first for unoriented rings and then for general 2-edge-connected graphs. These results establish that all graph problems are solvable in content-oblivious, 2-edge-connected networks. Much less is known about networks that are not 2-edge-connected. Censor-Hillel, Cohen, Gelles, and Sela showed that no non-constant function f(x,y) can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds x and the other holds y. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology G, leader election is possible in a wide range of graphs. Our main contributions are as follows: Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of G. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using O(n²) messages, where n is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter D = 2r, with message complexity O(nr). Necessity of topology knowledge: In the family of graphs 𝒢 = {P₃, P₅}, both the 3-path P₃ and the 5-path P₅ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to 𝒢, then terminating leader election is impossible.
Cite as

Yi-Jun Chang, Lyuting Chen, and Haoran Zhou. Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{chang_et_al:LIPIcs.ITCS.2026.36,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Zhou, Haoran},
  title =	{{Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{36:1--36:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.36},
  URN =		{urn:nbn:de:0030-drops-253239},
  doi =		{10.4230/LIPIcs.ITCS.2026.36},
  annote =	{Keywords: Asynchronous model, fault tolerance, quiescent termination}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.30
Byzantine-Tolerant Phase Clock

Authors: Costas Busch, Paweł Garncarek, and Dariusz R. Kowalski

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
A phase clock is a basic synchronization mechanism that keeps distributed nodes closely synchronized to execute the same phase of a distributed algorithm. A phase clock is typically implemented with a local logical counter that keeps track of the current phase count. Phase clocks are particularly useful in population protocols for implementing leader election and majority selection. We study phase clocks that tolerate Byzantine faults. We show that there is a phase clock that tolerates up to f < n/3 faulty nodes, where n is the number of nodes, such that the gap of the local counter values is O(n²log n). The gap can be further lowered to O(log n) when f ≤ n/8. We also show that if f > n/3, then the gap grows to infinity as time increases. While analyzing phase clock we introduce novel techniques and bounds for balls into bins processes, which might be of independent interest. Using the phase clock, we obtain a majority selection population protocol that tolerates up to f faults and decides on the majority value in O(log² n) parallel time using poly-log states per node.
Cite as

Costas Busch, Paweł Garncarek, and Dariusz R. Kowalski. Byzantine-Tolerant Phase Clock. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{busch_et_al:LIPIcs.OPODIS.2025.30,
  author =	{Busch, Costas and Garncarek, Pawe{\l} and Kowalski, Dariusz R.},
  title =	{{Byzantine-Tolerant Phase Clock}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.30},
  URN =		{urn:nbn:de:0030-drops-252036},
  doi =		{10.4230/LIPIcs.OPODIS.2025.30},
  annote =	{Keywords: phase clock, Byzantine nodes, population protocols, balls into bins}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.27
On the h-Majority Dynamics with Many Opinions

Authors: Francesco d'Amore, Niccolò D'Archivio, George Giakkoupis, and Emanuele Natale

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We present the first upper bound on the convergence time to consensus of the well-known h-majority dynamics with k opinions, in the synchronous setting, for h and k that are both non-constant values. We suppose that, at the beginning of the process, there is some initial additive bias towards some plurality opinion, that is, there is an opinion that is supported by x nodes while any other opinion is supported by strictly fewer nodes. We prove that, with high probability, if the bias is ω(√x) and the initial plurality opinion is supported by at least x = ω(log n) nodes, then the process converges to plurality consensus in O(log n) rounds whenever h = ω(n log n / x). A main corollary is the following: if k = o(n / log n) and the process starts from an almost-balanced configuration with an initial bias of magnitude ω(√{n/k}) towards the initial plurality opinion, then any function h = ω(k log n) suffices to guarantee convergence to consensus in O(log n) rounds, with high probability. Our upper bound shows that the lower bound of Ω(k / h²) rounds to reach consensus given by Becchetti et al. (2017) cannot be pushed further than Ω̃(k / h). Moreover, the bias we require is asymptotically smaller than the Ω(√{nlog n}) bias that guarantees plurality consensus in the 3-majority dynamics: in our case, the required bias is at most any (arbitrarily small) function in ω(√x) for any value of k ≥ 2.
Cite as

Francesco d'Amore, Niccolò D'Archivio, George Giakkoupis, and Emanuele Natale. On the h-Majority Dynamics with Many Opinions. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{damore_et_al:LIPIcs.DISC.2025.27,
  author =	{d'Amore, Francesco and D'Archivio, Niccol\`{o} and Giakkoupis, George and Natale, Emanuele},
  title =	{{On the h-Majority Dynamics with Many Opinions}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.27},
  URN =		{urn:nbn:de:0030-drops-248448},
  doi =		{10.4230/LIPIcs.DISC.2025.27},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Markov Chains, Consensus Problem, Opinion dynamics, Plurality Consensus}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.21
Content-Oblivious Leader Election in 2-Edge-Connected Networks

Authors: Jérémie Chalopin, Yi-Jun Chang, Lyuting Chen, Giuseppe A. Di Luna, and Haoran Zhou

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022 & Distributed Computing 2023) studied fully-defective asynchronous networks, where communication channels may arbitrarily corrupt messages. The model is equivalent to content-oblivious computation, where nodes communicate solely via pulses. They showed that if the network is 2-edge-connected, then any algorithm for a noiseless setting can be simulated in the fully-defective setting; otherwise, no non-trivial computation is possible in the fully-defective setting. However, their simulation requires a predesignated leader, which they conjectured to be necessary for any non-trivial content-oblivious task. Recently, Frei, Gelles, Ghazy, and Nolin (DISC 2024) refuted this conjecture for the special case of oriented ring topology. They designed two asynchronous content-oblivious leader election algorithms with message complexity O(n ⋅ ID_{max}), where n is the number of nodes and ID_{max} is the maximum ID. The first algorithm stabilizes in unoriented rings without termination detection. The second algorithm quiescently terminates in oriented rings, thus enabling the execution of the simulation algorithm after leader election. In this work, we present two results: General 2-edge-connected topologies: First, we show an asynchronous content-oblivious leader election algorithm that quiescently terminates in any 2-edge-connected network with message complexity O(m ⋅ N ⋅ ID_{min}), where m is the number of edges, N is a known upper bound on the number of nodes, and ID_{min} is the smallest ID. Combined with the above simulation, this result shows that whenever a size bound N is known, any noiseless algorithm can be simulated in the fully-defective model without a preselected leader, fully refuting the conjecture. Unoriented rings: We then show that the knowledge of N can be dropped in unoriented ring topologies by presenting a quiescently terminating election algorithm with message complexity O(n ⋅ ID_{max}) that matches the previous bound. Consequently, this result constitutes a strict improvement over the previous state of the art and shows that, on rings, fully-defective and noiseless communication are computationally equivalent, with no additional assumptions.
Cite as

Jérémie Chalopin, Yi-Jun Chang, Lyuting Chen, Giuseppe A. Di Luna, and Haoran Zhou. Content-Oblivious Leader Election in 2-Edge-Connected Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chalopin_et_al:LIPIcs.DISC.2025.21,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chang, Yi-Jun and Chen, Lyuting and Di Luna, Giuseppe A. and Zhou, Haoran},
  title =	{{Content-Oblivious Leader Election in 2-Edge-Connected Networks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.21},
  URN =		{urn:nbn:de:0030-drops-248385},
  doi =		{10.4230/LIPIcs.DISC.2025.21},
  annote =	{Keywords: Asynchronous model, fault tolerance, quiescent termination}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.1
The Expressive Power of Uniform Population Protocols with Logarithmic Space

Authors: Philipp Czerner, Vincent Fischer, and Roland Guttenberg

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of states, research nowadays focuses on protocols where the space usage depends on the number of agents. The expressive power of population protocols has so far however only been determined for protocols using o(log n) states, which compute only semilinear predicates, and for Ω(n) states. This leaves a significant gap, particularly concerning protocols with Θ(log n) or Θ(polylog n) states, which are the most common constructions in the literature. In this paper we close the gap and prove that for any ε > 0 and f ∈ Ω(log n)∩𝒪(n^{1-ε}), both uniform and non-uniform population protocols with Θ(f(n)) states can decide exactly those predicates, whose unary encoding lies in NSPACE(f(n) log n).
Cite as

Philipp Czerner, Vincent Fischer, and Roland Guttenberg. The Expressive Power of Uniform Population Protocols with Logarithmic Space. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{czerner_et_al:LIPIcs.SAND.2025.1,
  author =	{Czerner, Philipp and Fischer, Vincent and Guttenberg, Roland},
  title =	{{The Expressive Power of Uniform Population Protocols with Logarithmic Space}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.1},
  URN =		{urn:nbn:de:0030-drops-230540},
  doi =		{10.4230/LIPIcs.SAND.2025.1},
  annote =	{Keywords: Population Protocols, Uniform, Expressive Power}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.36
Distributed Branching Random Walks and Their Applications

Authors: Vijeth Aradhya, Seth Gilbert, and Thorsten Götte

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
In recent years, the explosion of big data and analytics has necessitated distributed storage and processing with several compute nodes (e.g., multiple datacenters). These nodes collaboratively perform parallel computation, where the data is typically partitioned across these nodes to ensure scalability, redundancy and load-balancing. But the nodes may not always be co-located; in many cases, they are part of a larger communication network. Since those nodes only need to communicate among themselves, a key challenge is to design efficient routes catered to that subnetwork. In this work, we initiate the study of distributed sampling and routing problems for subnetworks in any well-connected network. Given any network G = (V, E) with mixing time τ_mix, consider the canonical problem of permutation routing [Ghaffari, Kuhn and Su, PODC 2017] that aims to minimize both congestion and dilation of the routes, where the demands (i.e., set of source-terminal pairs) are such that each node sends or receives number of messages proportional to its degree. We show that the permutation routing problem, when demands are restricted to any subset S ⊆ V (i.e., subnetwork), can be solved in exp(O(√(log|S|))) ⋅ Õ(τ_mix) rounds (where Õ(⋅) hides polylogarithmic factors of |V|). This means that the running time depends subpolynomially on the subnetwork size (i.e., not on the entire network size). The ability to solve permutation routing efficiently immediately implies that a large class of parallel algorithms can be simulated efficiently on the subnetwork. As a prerequisite to constructing efficient routes, we design and analyze distributed branching random walks that distribute tokens started by the nodes in the subnetwork. At a high-level, these algorithms operate by always moving each token according to a (lazy) simple random walk, but also branching a token into multiple tokens at some specified intervals; ultimately, if a node starts a branching walk, with its id in a token, then by the end of execution, several tokens with its id would be randomly distributed among the nodes. As these random walks can be started by many nodes, a crucial challenge is to ensure low-congestion, which is a primary focus of this paper.
Cite as

Vijeth Aradhya, Seth Gilbert, and Thorsten Götte. Distributed Branching Random Walks and Their Applications. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{aradhya_et_al:LIPIcs.OPODIS.2024.36,
  author =	{Aradhya, Vijeth and Gilbert, Seth and G\"{o}tte, Thorsten},
  title =	{{Distributed Branching Random Walks and Their Applications}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.36},
  URN =		{urn:nbn:de:0030-drops-225723},
  doi =		{10.4230/LIPIcs.OPODIS.2024.36},
  annote =	{Keywords: Distributed Graph Algorithms, Random Walks, Permutation Routing}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.37
Almost Time-Optimal Loosely-Stabilizing Leader Election on Arbitrary Graphs Without Identifiers in Population Protocols

Authors: Haruki Kanaya, Ryota Eguchi, Taisho Sasada, and Michiko Inoue

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
The population protocol model is a computational model for passive mobile agents. We address the leader election problem, which determines a unique leader on arbitrary communication graphs starting from any configuration. Unfortunately, self-stabilizing leader election is impossible to be solved without knowing the exact number of agents; thus, we consider loosely-stabilizing leader election, which converges to safe configurations in a relatively short time, and holds the specification (maintains a unique leader) for a relatively long time. When agents have unique identifiers, Sudo {et al. }(2019) proposed a protocol that, given an upper bound N for the number of agents n, converges in O(mNlog n) expected steps, where m is the number of edges. When unique identifiers are not required, they also proposed a protocol that, using random numbers and given N, converges in O(mN²log{N}) expected steps. Both protocols have a holding time of Ω(e^{2N}) expected steps and use O(log{N}) bits of memory. They also showed that the lower bound of the convergence time is Ω(mN) expected steps for protocols with a holding time of Ω(e^N) expected steps given N. In this paper, we propose protocols that do not require unique identifiers. These protocols achieve convergence times close to the lower bound with increasing memory usage. Specifically, given N and an upper bound Δ for the maximum degree, we propose two protocols whose convergence times are O(mNlog n) and O(mNlog N) both in expectation and with high probability. The former protocol uses random numbers, while the latter does not require them. Both protocols utilize O(Δ log N) bits of memory and hold the specification for Ω(e^{2N}) expected steps.
Cite as

Haruki Kanaya, Ryota Eguchi, Taisho Sasada, and Michiko Inoue. Almost Time-Optimal Loosely-Stabilizing Leader Election on Arbitrary Graphs Without Identifiers in Population Protocols. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{kanaya_et_al:LIPIcs.OPODIS.2024.37,
  author =	{Kanaya, Haruki and Eguchi, Ryota and Sasada, Taisho and Inoue, Michiko},
  title =	{{Almost Time-Optimal Loosely-Stabilizing Leader Election on Arbitrary Graphs Without Identifiers in Population Protocols}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.37},
  URN =		{urn:nbn:de:0030-drops-225734},
  doi =		{10.4230/LIPIcs.OPODIS.2024.37},
  annote =	{Keywords: Population protocols, Leader election, Loose-stabilization, Self-stabilization}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.13
Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility

Authors: Raphael Gerlach, Sören von der Gracht, Christopher Hahn, Jonas Harbig, and Peter Kling

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
In the general pattern formation (GPF) problem, a swarm of simple autonomous, disoriented robots must form a given pattern. The robots' simplicity imply a strong limitation: When the initial configuration is rotationally symmetric, only patterns with a similar symmetry can be formed [Masafumi Yamashita and Ichiro Suzuki, 2010]. The only known algorithm to form large patterns with limited visibility and without memory requires the robots to start in a near-gathering (a swarm of constant diameter) [Christopher Hahn et al., 2024]. However, not only do we not know any near-gathering algorithm guaranteed to preserve symmetry but most natural gathering strategies trivially increase symmetries [Jannik Castenow et al., 2022]. Thus, we study near-gathering without changing the swarm’s rotational symmetry for disoriented, oblivious robots with limited visibility (the OBLOT-model, see [Paola Flocchini et al., 2019]). We introduce a technique based on the theory of dynamical systems to analyze how a given algorithm affects symmetry and provide sufficient conditions for symmetry preservation. Until now, it was unknown whether the considered OBLOT-model allows for any non-trivial algorithm that always preserves symmetry. Our first result shows that a variant of Go-To-The-Average always preserves symmetry but may sometimes lead to multiple, unconnected near-gathering clusters. Our second result is a symmetry-preserving near-gathering algorithm that works on swarms with a convex boundary (the outer boundary of the unit disc graph) and without "holes" (circles of diameter 1 inside the boundary without any robots).
Cite as

Raphael Gerlach, Sören von der Gracht, Christopher Hahn, Jonas Harbig, and Peter Kling. Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 13:1-13:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{gerlach_et_al:LIPIcs.OPODIS.2024.13,
  author =	{Gerlach, Raphael and von der Gracht, S\"{o}ren and Hahn, Christopher and Harbig, Jonas and Kling, Peter},
  title =	{{Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{13:1--13:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.13},
  URN =		{urn:nbn:de:0030-drops-225490},
  doi =		{10.4230/LIPIcs.OPODIS.2024.13},
  annote =	{Keywords: Swarm Algorithm, Swarm Robots, Distributed Algorithm, Pattern Formation, Limited Visibility, Oblivious}
}
Document
DOI: 10.4230/LIPIcs.SAND.2024.14
Forming Large Patterns with Local Robots in the OBLOT Model

Authors: Christopher Hahn, Jonas Harbig, and Peter Kling

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
In the arbitrary pattern formation problem, n autonomous, mobile robots must form an arbitrary pattern P ⊆ R². The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form P under a natural symmetry condition if robots have no memory but an unlimited viewing range [Masafumi Yamashita and Ichiro Suzuki, 2010] or if robots have a limited viewing range but memory [Yukiko Yamauchi and Masafumi Yamashita, 2013]. In the latter case, P is only formed in a shrunk version that has constant diameter. Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that P can be formed under the same symmetry condition if the robots' initial diameter is ≤ 1. Our protocol partitions P into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while "drawing" P by dropping one robot per pattern coordinate.
Cite as

Christopher Hahn, Jonas Harbig, and Peter Kling. Forming Large Patterns with Local Robots in the OBLOT Model. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{hahn_et_al:LIPIcs.SAND.2024.14,
  author =	{Hahn, Christopher and Harbig, Jonas and Kling, Peter},
  title =	{{Forming Large Patterns with Local Robots in the OBLOT Model}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.14},
  URN =		{urn:nbn:de:0030-drops-198924},
  doi =		{10.4230/LIPIcs.SAND.2024.14},
  annote =	{Keywords: Swarm Algorithm, Swarm Robots, Distributed Algorithm, Pattern Formation, Limited Visibility, Oblivious}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.38
Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings

Authors: Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, [Christoph Dürr et al., 2020] has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a (4+ε)-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a (2+ε)-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time 𝒪(poly(n/ε)). Lastly, we show that our results are essentially optimal by providing matching lower bounds.
Cite as

Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang. Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{damerius_et_al:LIPIcs.ESA.2023.38,
  author =	{Damerius, Christoph and Kling, Peter and Li, Minming and Xu, Chenyang and Zhang, Ruilong},
  title =	{{Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{38:1--38:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.38},
  URN =		{urn:nbn:de:0030-drops-186915},
  doi =		{10.4230/LIPIcs.ESA.2023.38},
  annote =	{Keywords: scheduling, total completion time, makespan, LP rounding, competitive analysis, approximation algorithm, NP hardness, PTAS}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2022.15
A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility

Authors: Jannik Castenow, Jonas Harbig, Daniel Jung, Peter Kling, Till Knollmann, and Friedhelm Meyer auf der Heide

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
We consider a swarm of n robots in a d-dimensional Euclidean space. The robots are oblivious (no persistent memory), disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task Gathering requires that all robots reach the same, not predefined position. In the related NearGathering task, they must reach distinct positions in close proximity such that every robot sees the entire swarm. In the considered setting, Gathering can be solved in 𝒪(n + Δ²) synchronous rounds both in two and three dimensions, where Δ denotes the initial maximal distance of two robots [Hideki Ando et al., 1999; Michael Braun et al., 2020; Bastian Degener et al., 2011]. In this work, we formalize a key property of efficient Gathering protocols and use it to define λ-contracting protocols. Any such protocol gathers n robots in the d-dimensional space in 𝒪(Δ²) synchronous rounds, for d ≥ 2. For d = 1, any λ-contracting protocol gathers in optimal time 𝒪(Δ). Moreover, we prove a corresponding lower bound stating that any protocol in which robots move to target points inside the local convex hulls of their neighborhoods - λ-contracting protocols have this property - requires Ω(Δ²) rounds to gather all robots (d > 1). Among others, we prove that the d-dimensional generalization of the GTC-protocol [Hideki Ando et al., 1999] is λ-contracting. Remarkably, our improved and generalized runtime bound is independent of n and d. We also introduce an approach to make any λ-contracting protocol collision-free (robots never occupy the same position) to solve NearGathering. The resulting protocols maintain the runtime of Θ (Δ²) and work even in the semi-synchronous model. This yields the first NearGathering protocols for disoriented robots and the first proven runtime bound. In particular, combined with results from [Paola Flocchini et al., 2017] for robots with global visibility, we obtain the first protocol to solve Uniform Circle Formation (arrange the robots on the vertices of a regular n-gon) for oblivious, disoriented robots with limited visibility.
Cite as

Jannik Castenow, Jonas Harbig, Daniel Jung, Peter Kling, Till Knollmann, and Friedhelm Meyer auf der Heide. A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 15:1-15:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{castenow_et_al:LIPIcs.OPODIS.2022.15,
  author =	{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm},
  title =	{{A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{15:1--15:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.15},
  URN =		{urn:nbn:de:0030-drops-176350},
  doi =		{10.4230/LIPIcs.OPODIS.2022.15},
  annote =	{Keywords: mobile robots, gathering, limited visibility, runtime, collision avoidance, near-gathering}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.18
Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

Authors: Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, and Andreas Wiese

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of maximum total value that can be packed into the knapsacks without exceeding the capacities. We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing input. More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items. As the optimal and any approximate solution may change drastically, we maintain implicit solutions and support polylogarithmic time query operations that can return the computed solution value and the packing of any given item. While dynamic algorithms are well-studied in the context of graph problems, there is hardly any work on packing problems (and generally much less on non-graph problems). Motivated by the theoretical interest in knapsack problems and their practical relevance, our work bridges this gap.
Cite as

Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, and Andreas Wiese. Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{eberle_et_al:LIPIcs.FSTTCS.2021.18,
  author =	{Eberle, Franziska and Megow, Nicole and N\"{o}lke, Lukas and Simon, Bertrand and Wiese, Andreas},
  title =	{{Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.18},
  URN =		{urn:nbn:de:0030-drops-155297},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.18},
  annote =	{Keywords: Fully dynamic algorithms, knapsack problem, approximation schemes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.61
On Greedily Packing Anchored Rectangles

Authors: Christoph Damerius, Dominik Kaaser, Peter Kling, and Florian Schneider

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
Consider a set P of points in the unit square U = [1,0), one of them being the origin. For each point p ∈ P you may draw an axis-aligned rectangle in U with its lower-left corner being p. What is the maximum area such rectangles can cover without overlapping each other? Freedman posed this problem in 1969, asking whether one can always cover at least 50% of U. Over 40 years later, Dumitrescu and Tóth [Adrian Dumitrescu and Csaba D. Tóth, 2015] achieved the first constant coverage of 9.1%; since then, no significant progress was made. While 9.1% might seem low, the authors could not find any instance where their algorithm covers less than 50%, nourishing the hope to eventually prove a 50% bound. While we indeed significantly raise the algorithm’s coverage to 39%, we extinguish the hope of reaching 50% by giving points for which its coverage stays below 43.3%. Our analysis studies the algorithm’s average and worst-case density of so-called tiles, which represent the staircase polygons in which a point can freely choose its maximum-area rectangle. Our approach is comparatively general and may potentially help in analyzing related algorithms.
Cite as

Christoph Damerius, Dominik Kaaser, Peter Kling, and Florian Schneider. On Greedily Packing Anchored Rectangles. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 61:1-61:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{damerius_et_al:LIPIcs.ICALP.2021.61,
  author =	{Damerius, Christoph and Kaaser, Dominik and Kling, Peter and Schneider, Florian},
  title =	{{On Greedily Packing Anchored Rectangles}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{61:1--61:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.61},
  URN =		{urn:nbn:de:0030-drops-141306},
  doi =		{10.4230/LIPIcs.ICALP.2021.61},
  annote =	{Keywords: lower-left anchored rectangle packing, greedy algorithm, charging scheme}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.8
On the Complexity of Anchored Rectangle Packing

Authors: Antonios Antoniadis, Felix Biermeier, Andrés Cristi, Christoph Damerius, Ruben Hoeksma, Dominik Kaaser, Peter Kling, and Lukas Nölke

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

Abstract
In the Anchored Rectangle Packing (ARP) problem, we are given a set of points P in the unit square [0,1]^2 and seek a maximum-area set of axis-aligned interior-disjoint rectangles S, each of which is anchored at a point p in P. In the most prominent variant - Lower-Left-Anchored Rectangle Packing (LLARP) - rectangles are anchored in their lower-left corner. Freedman [W. T. Tutte (Ed.), 1969] conjectured in 1969 that, if (0,0) in P, then there is a LLARP that covers an area of at least 0.5. Somewhat surprisingly, this conjecture remains open to this day, with the best known result covering an area of 0.091 [Dumitrescu and Tóth, 2015]. Maybe even more surprisingly, it is not known whether LLARP - or any ARP-problem with only one anchor - is NP-hard. In this work, we first study the Center-Anchored Rectangle Packing (CARP) problem, where rectangles are anchored in their center. We prove NP-hardness and provide a PTAS. In fact, our PTAS applies to any ARP problem where the anchor lies in the interior of the rectangles. Afterwards, we turn to the LLARP problem and investigate two different resource-augmentation settings: In the first we allow an epsilon-perturbation of the input P, whereas in the second we permit an epsilon-overlap between rectangles. For the former setting, we give an algorithm that covers at least as much area as an optimal solution of the original problem. For the latter, we give an (1 - epsilon)-approximation.
Cite as

Antonios Antoniadis, Felix Biermeier, Andrés Cristi, Christoph Damerius, Ruben Hoeksma, Dominik Kaaser, Peter Kling, and Lukas Nölke. On the Complexity of Anchored Rectangle Packing. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{antoniadis_et_al:LIPIcs.ESA.2019.8,
  author =	{Antoniadis, Antonios and Biermeier, Felix and Cristi, Andr\'{e}s and Damerius, Christoph and Hoeksma, Ruben and Kaaser, Dominik and Kling, Peter and N\"{o}lke, Lukas},
  title =	{{On the Complexity of Anchored Rectangle Packing}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{8:1--8:14},
  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.2019.8},
  URN =		{urn:nbn:de:0030-drops-111297},
  doi =		{10.4230/LIPIcs.ESA.2019.8},
  annote =	{Keywords: anchored rectangle, rectangle packing, resource augmentation, PTAS, NP, hardness}
}
  • Refine by Type
  • 20 Document/PDF
  • 9 Document/HTML

  • Refine by Publication Year
  • 3 2026
  • 6 2025
  • 1 2024
  • 2 2023
  • 2 2021
  • Show More...

  • Refine by Author
  • 11 Kling, Peter
  • 4 Berenbrink, Petra
  • 4 Kaaser, Dominik
  • 3 Damerius, Christoph
  • 3 Friedetzky, Tom
  • Show More...

  • Refine by Series/Journal
  • 19 LIPIcs
  • 1 OASIcs

  • Refine by Classification
  • 7 Theory of computation → Distributed algorithms
  • 2 Theory of computation → Distributed computing models
  • 2 Theory of computation → Packing and covering problems
  • 2 Theory of computation → Random walks and Markov chains
  • 2 Theory of computation → Self-organization
  • Show More...

  • Refine by Keyword
  • 2 Asynchronous model
  • 2 Distributed Algorithm
  • 2 Limited Visibility
  • 2 Oblivious
  • 2 PTAS
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact