14 Search Results for "Stachowiak, Grzegorz"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.31
Improved and Parameterized Algorithms for Online Multi-Level Aggregation

Authors: Young-San Lin and Alex Turoczy

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We study the online multi-level aggregation problem with deadlines (MLAP-D) introduced by Bienkowski, Böhm, Byrka, Chrobak, Dürr, Folwarczný, Jeż, Sgall, Thang, and Veselý (ESA 2016, OR 2020). In this problem, requests arrive over time at the vertices of a given vertex-weighted tree, and each request has a deadline that it must be served by. The cost of serving a request equals the cost of a path from the root to the vertex where the request resides. Instead of serving each request individually, requests can be aggregated and served by transmitting a subtree from the root that spans the vertices on which the requests reside, to potentially be more cost-effective. The aggregated cost is the weight of the transmission subtree. The goal of MLAP-D is to find an aggregation solution that minimizes the total cost while serving all requests. MLAP-D generalizes some well-studied problems including the TCP acknowledgment problem and the joint replenishment problem, and arises in natural scenarios such as multi-casting, sensor networks, and supply chain management. We present improved and parameterized algorithms for MLAP-D. Our result is twofold. First, we present an e(D+1)-competitive algorithm where D is the depth of the tree. Second, we present an e(4H+2)-competitive algorithm where H is the caterpillar dimension of the tree. Here, H ≤ D and H ≤ log₂ |V| where |V| is the number of vertices in the given tree. The caterpillar dimension remains constant for rich but simple classes of trees, such as line graphs (H = 1), caterpillar graphs (H = 2), and lobster graphs (H = 3). To the best of our knowledge, this is the first online algorithm parameterized on a measure better than depth. The state-of-the-art online algorithms are 6(D+1)-competitive by Buchbinder, Feldman, Naor, and Talmon (SODA 2017) and O(log |V|)-competitive by Azar and Touitou (FOCS 2020). Our framework outperforms the state-of-the-art ratios when H = o(min{D,log₂ |V|}). Our memory-based algorithms extend transmission subtrees with a cost comparable to transmission subtrees used to serve previous requests. Our simple framework directly applies to trees with any structure and differs from the previous frameworks that reduce the problem to trees with specific structures.
Cite as

Young-San Lin and Alex Turoczy. Improved and Parameterized Algorithms for Online Multi-Level Aggregation. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lin_et_al:LIPIcs.SWAT.2026.31,
  author =	{Lin, Young-San and Turoczy, Alex},
  title =	{{Improved and Parameterized Algorithms for Online Multi-Level Aggregation}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.31},
  URN =		{urn:nbn:de:0030-drops-260673},
  doi =		{10.4230/LIPIcs.SWAT.2026.31},
  annote =	{Keywords: Online Algorithms, Approximation Algorithms, Graph Problems}
}
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)

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@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.ISAAC.2025.35
Anonymous Self-Stabilising Localisation via Spatial Population Protocols

Authors: Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak

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

Abstract
In the distributed localisation problem (DLP), n anonymous robots (agents) A_0, ..., A_{n-1} are located at arbitrary points p_0, ..., p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified (jointly agreed) coordinate system, in which all agents receive unique labels (coordinates) that accurately reflect the relative distances between all points p_0, ..., p_{n-1} in S. Extensive research on DLP has primarily focus on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In contrast, this paper proposes a minimalist, computationally efficient distributed computing model where agents can query any pairwise relative positions, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v_{ij} spanning points p_i and p_j (vector query model). We propose and analyse several distributed localisation protocols, including: 1) Leader-based localisation protocol with distance queries We propose and analyse two leader-based localisation protocols that stabilise silently in o(n) time. These protocols leverage an efficient solution to the novel concept of multi-contact epidemic, a natural generalisation of the core communication tool in population protocols, known as the one-way epidemic. 2) Self-stabilising leader localisation protocol with distance queries We show how to effectively utilise a leader election mechanism within the leader-based localisation protocol to get a DLP protocol that self-stabilises silently in time O(n(log n/n)^{1/(k+1)}log n) in k-dimensions. 3) Self-stabilising localisation protocol with vector queries We propose and analyse an optimally fast DLP protocol which self-stabilises silently in O(log n) time.
Cite as

Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Anonymous Self-Stabilising Localisation via Spatial Population Protocols. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gasieniec_et_al:LIPIcs.ISAAC.2025.35,
  author =	{G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Anonymous Self-Stabilising Localisation via Spatial Population Protocols}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.35},
  URN =		{urn:nbn:de:0030-drops-249433},
  doi =		{10.4230/LIPIcs.ISAAC.2025.35},
  annote =	{Keywords: Population Protocols, Distributed Localisation, Spacial Queries, Self-Stabilisation}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.33
Approach of Agents with Restricted Fuel Tanks

Authors: Adam Ganczorz, Tomasz Jurdzinski, Andrzej Pelc, and Grzegorz Stachowiak

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

Abstract
Two mobile agents, modelled as points in the plane moving at speed 1, have to get at a distance at most 1 from each other. This task is known as approach or rendezvous in the plane. An adversary initially places both agents at distinct points, called their bases, at distance at most D, and wakes them up at possibly different times. Each of the agents has a fuel tank that allows them to traverse a trajectory of length D, and can be replenished at the base of the agent. The algorithm of each agent consists of a series of actions which are either moves at a chosen distance in a chosen direction or staying idle for a chosen period of time. For a given instance of the approach task, the execution time of an approach algorithm is the length of the period between the start of the later agent and the moment of approach. Our goal is to design approach algorithms with optimal time complexity. We consider two independent coherence assumptions. One of them is time coherence, i.e., agents start simultaneously, and the other is orientation coherence: agents have compatible compasses, showing the same North direction. Our main result is establishing optimal time complexity of the approach problem with restricted fuel tanks. It turns out that this optimal complexity heavily depends on the above coherence assumptions. If both of them are satisfied then approach can be performed in time O(D²) and we show that this complexity is optimal. If any of the two coherence assumptions is missing then approach can be performed in time O(D²√D) and we prove that this order of magnitude cannot be improved. Our main technical contribution are lower bounds showing that, for each of the considered scenarios, our fairly natural approach algorithms are, in fact, optimal.
Cite as

Adam Ganczorz, Tomasz Jurdzinski, Andrzej Pelc, and Grzegorz Stachowiak. Approach of Agents with Restricted Fuel Tanks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2025.33,
  author =	{Ganczorz, Adam and Jurdzinski, Tomasz and Pelc, Andrzej and Stachowiak, Grzegorz},
  title =	{{Approach of Agents with Restricted Fuel Tanks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{33:1--33:22},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-248506},
  doi =		{10.4230/LIPIcs.DISC.2025.33},
  annote =	{Keywords: mobile agent, approach, rendezvous, plane, restricted energy}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.65
Ultra-Resilient Superimposed Codes: Near-Optimal Construction and Applications

Authors: Gianluca De Marco and Dariusz R. Kowalski

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

Abstract
A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any k others, enabling unique identification of codewords within any group of k. Superimposed codes are foundational combinatorial tools with applications in areas ranging from distributed computing and data retrieval to fault-tolerant communication. However, classical superimposed codes rely on strict alignment assumptions, limiting their effectiveness in asynchronous and fault-prone environments, which are common in modern systems and applications. We introduce Ultra-Resilient Superimposed Codes (URSCs), a new class of codes that extends the classic superimposed framework by ensuring a stronger codewords' isolation property and resilience to two types of adversarial perturbations: arbitrary cyclic shifts and partial bitwise corruption (flips). Additionally, URSCs exhibit universality, adapting seamlessly to any number k of concurrent codewords without prior knowledge. This is a combination of properties not achieved in any previous construction. We provide the first polynomial-time construction of URSCs with near-optimal length, significantly outperforming previous constructions with less general features, all without requiring prior knowledge of the number of concurrent codewords, k. We demonstrate that our URSCs significantly advance the state of the art in multiple applications, including uncoordinated beeping networks, where our codes reduce time complexity for local broadcast by nearly two orders of magnitude, and generalized contention resolution in multi-access channel communication.
Cite as

Gianluca De Marco and Dariusz R. Kowalski. Ultra-Resilient Superimposed Codes: Near-Optimal Construction and Applications. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{demarco_et_al:LIPIcs.ICALP.2025.65,
  author =	{De Marco, Gianluca and Kowalski, Dariusz R.},
  title =	{{Ultra-Resilient Superimposed Codes: Near-Optimal Construction and Applications}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{65:1--65:20},
  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.2025.65},
  URN =		{urn:nbn:de:0030-drops-234429},
  doi =		{10.4230/LIPIcs.ICALP.2025.65},
  annote =	{Keywords: superimposed codes, ultra-resiliency, deterministic algorithms, uncoordinated beeping networks, contention resolution}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.19
Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols

Authors: Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak

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

Abstract
In the distributed localization problem (DLP), n anonymous robots (agents) A₀, …, A_{n-1} begin at arbitrary positions p₀, …, p_{n-1} ∈ S, where S is a Euclidean space. Initially, each agent A_i operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified coordinate system that accurately reflects the relative positions of all points, p₀, …, p_{n-1}, in S. Extensive research on DLP has primarily focused on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In this paper, however, we examine a minimalist, computationally efficient model of distributed computing in which agents have access to all pairwise distances, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A_i and A_j interact, they can not only exchange their current knowledge but also either determine the distance d_{ij} between them in S (distance query model) or obtain the vector v→_{ij} spanning points p_i and p_j (vector query model). We present here a leader-based localisation protocol with distance queries.
Cite as

Leszek Gąsieniec, Łukasz Kuszner, Ehsan Latif, Ramviyas Parasuraman, Paul Spirakis, and Grzegorz Stachowiak. Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 19:1-19:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gasieniec_et_al:LIPIcs.SAND.2025.19,
  author =	{G\k{a}sieniec, Leszek and Kuszner, {\L}ukasz and Latif, Ehsan and Parasuraman, Ramviyas and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Brief Announcement: Anonymous Distributed Localisation via Spatial Population Protocols}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{19:1--19:5},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-230726},
  doi =		{10.4230/LIPIcs.SAND.2025.19},
  annote =	{Keywords: Population Protocols, Distributed Localisation}
}
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)

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@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.2024.37
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)

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@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.STACS.2023.33
New Clocks, Optimal Line Formation and Self-Replication Population Protocols

Authors: Leszek Gąsieniec, Paul G. Spirakis, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
In this paper we consider a known variant of the standard population protocol model in which agents are allowed to be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ(n²) interactions in expectation which coincides with Θ(n) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O(polylog n) parallel time. The main focus of this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model. - We propose and analyze a novel edge based phase clock counting parallel time Θ(nlog n) in the network constructor model, showing also that its leader based counterpart provides the same time guarantees in the standard population protocol model. Note that all currently known phase clocks can count parallel time not exceeding O(polylog n). - We prove that any spanning line formation protocol requires Ω(nlog n) parallel time if high probability guaranty is imposed. We also show that the new clock enables an optimal O(nlog n) parallel time spanning line construction, which improves dramatically on the best currently known O(n²) parallel time protocol, solving the main open problem in the considered model [O. Michail and P. Spirakis, 2016]. - We propose a new probabilistic bubble-sort algorithm in which random comparisons and transfers are limited to the adjacent positions in the sequence. Utilising a novel potential function reasoning we show that rather surprisingly this probabilistic sorting procedure requires O(n²) comparisons in expectation and whp, and is on par with its deterministic counterpart. - We propose the first population protocol allowing self-replication of a strand of an arbitrary length k (carrying k-bit message of size independent of the state space) in parallel time O(n(k+log n)). The bit pipelining mechanism and the time complexity analysis of self-replication process mimic those used in the probabilistic bubble-sort argument. The new protocol permits also simultaneous self-replication, where l copies of the strand can be created in parallel in time O(n(k+log n)log l). We also discuss application of the strand self-replication protocol to pattern matching. All protocols are always correct and provide time guarantees with high probability defined as 1-n^(-η), for a constant η > 0.
Cite as

Leszek Gąsieniec, Paul G. Spirakis, and Grzegorz Stachowiak. New Clocks, Optimal Line Formation and Self-Replication Population Protocols. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gasieniec_et_al:LIPIcs.STACS.2023.33,
  author =	{G\k{a}sieniec, Leszek and Spirakis, Paul G. and Stachowiak, Grzegorz},
  title =	{{New Clocks, Optimal Line Formation and Self-Replication Population Protocols}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{33:1--33:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.33},
  URN =		{urn:nbn:de:0030-drops-176857},
  doi =		{10.4230/LIPIcs.STACS.2023.33},
  annote =	{Keywords: Population protocols, constructors, probabilistic bubble-sort, self-replication}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.17
Contention Resolution Without Collision Detection: Constant Throughput And Logarithmic Energy

Authors: Gianluca De Marco, Dariusz R. Kowalski, and Grzegorz Stachowiak

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

Abstract
A shared channel, also called a multiple access channel, is among the most popular and widely studied models of communication in distributed computing. An unknown number of stations (potentially unbounded) is connected to the channel and can communicate by transmitting and listening. A message is successfully transmitted on the channel if and only if there is a unique transmitter at that time; otherwise the message collides with some other transmission and nothing is sensed by the participating stations. We consider the general framework without collision detection and in which any participating station can join the channel at any moment. The contention resolution task is to let each of the contending stations to broadcast successfully its message on the channel. In this setting we present the first algorithm which exhibits asymptotically optimal Θ(1) throughput and only an O(log k) energy cost, understood as the maximum number of transmissions performed by a single station (where k is the number of participating stations, initially unknown). We also show that such efficiency cannot be reproduced by non-adaptive algorithms, i.e., whose behavior does not depend on the channel history (for example, classic backoff protocols). Namely, we show that non-adaptive algorithms cannot simultaneously achieve throughput Ω(1/polylog(k)) and energy O((log² k)/(log log k)²).
Cite as

Gianluca De Marco, Dariusz R. Kowalski, and Grzegorz Stachowiak. Contention Resolution Without Collision Detection: Constant Throughput And Logarithmic Energy. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{demarco_et_al:LIPIcs.DISC.2022.17,
  author =	{De Marco, Gianluca and Kowalski, Dariusz R. and Stachowiak, Grzegorz},
  title =	{{Contention Resolution Without Collision Detection: Constant Throughput And Logarithmic Energy}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{17:1--17:21},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.17},
  URN =		{urn:nbn:de:0030-drops-172081},
  doi =		{10.4230/LIPIcs.DISC.2022.17},
  annote =	{Keywords: Shared channel, Contention resolution, Throughput, Energy consumption, Randomized algorithms, Lower bound}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.44
Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols

Authors: Leszek Gąsieniec, Paul Spirakis, and Grzegorz Stachowiak

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

Abstract
In this paper we consider a known variant of the standard population protocol model in which agents can be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. The state space of agents is fixed (constant size) and the size n of the population is not known, i.e., not hard-coded in the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ(n²) interactions in expectation which coincides with Θ(n) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O(polylog n) parallel time. The main focus in this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model. - We propose and analyse a novel edge based phase clock counting parallel time Θ(nlog n) in the network constructor model, showing also that its leader based counterpart provides the same time guaranties in the standard population protocol model. Note that all currently known phase clocks can count parallel time not exceeding O(polylog n). - The new clock enables a nearly optimal O(nlog n) parallel time spanning line construction (a key component of universal network construction), which improves dramatically on the best currently known O(n²) parallel time protocol, solving the main open problem in the considered model [O. Michail and P. Spirakis, 2016]. - We propose a new probabilistic bubble-sort algorithm in which random comparisons and transfers are allowed only between the adjacent positions in the sequence. Utilising a novel potential function reasoning we show that rather surprisingly this probabilistic sorting (via conditional pipelining) procedure requires O(n²) comparisons in expectation and whp, and is on par with its deterministic counterpart. - We propose the first population protocol allowing self-replication of a strand of an arbitrary length k (carrying a k-bit message of size independent of the state space) in parallel time O(n(k+log n)). The pipelining mechanism and the time complexity analysis of the strand self-replication protocol mimic those used in the probabilistic bubble-sort. The new protocol permits also simultaneous self-replication, where l copies of the strand can be created in time O(n(k+log n)log l). Finally, we discuss application of the strand self-replication protocol to pattern matching. Our protocols are always correct and provide time guaranties with high probability defined as 1-n^{-η}, for a constant η > 0.
Cite as

Leszek Gąsieniec, Paul Spirakis, and Grzegorz Stachowiak. Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 44:1-44:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gasieniec_et_al:LIPIcs.DISC.2022.44,
  author =	{G\k{a}sieniec, Leszek and Spirakis, Paul and Stachowiak, Grzegorz},
  title =	{{Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{44:1--44:3},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.44},
  URN =		{urn:nbn:de:0030-drops-172351},
  doi =		{10.4230/LIPIcs.DISC.2022.44},
  annote =	{Keywords: Population protocols, network constructors, probabilistic bubble-sort, self-replication}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.SWAT.2022.2
Time, Clocks and Efficiency of Population Protocols (Invited Paper)

Authors: Leszek Gąsieniec and Grzegorz Stachowiak

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

Abstract
The model of population protocols is used to study distributed processes based on pairwise interactions between simple anonymous agents drawn from a large population of size n. The order in which agents meet in pairs is determined by the random scheduler, s.t., each consecutive pair is chosen uniformly at random. After each interaction the state of the relevant agents are amended according to the predefined transition function (the actual code of the algorithm) which governs the considered process. The state space of agents is often fixed and the size n is not known in advance, i.e., not hard-coded in the transition function. We assume that a population protocol starts in the predefined initial configuration of agents' states representing the input. And if successful, the protocol stabilises in a final configuration of states forming the output representing the solution to the considered problem. The time complexity of a population protocol refers to the number of interactions required to stabilise this protocol in a final configuration. We also define parallel time as the time complexity divided by n. Note that the parallel time of the system and the expected local time of each agent, i.e., the number of interactions observed by each agent, are correlated. Several mechanisms, known as phase clocks, have been developed to measure parallel time more accurately than counting local interactions. Most of the clocks target counting Θ(log n) parallel time required to fully synchronise all agents in the population. There are leader (and junta) based phase clocks which utilise a fixed number of states [D. Angluin et al., 2008; L. Gąsieniec and G. Stachowiak, 2021]. This type of clocks allows also counting any poly-logarithmic time while preserving fix state utilisation. The other type refers to leaderless clocks utilising Θ(log n) states [D. Alistarh et al., 2018; D. Doty et al., 2021]. This type allows approximate counting of parallel time as fixed resolution clocks [D. Doty et al., 2021] or oscillators [D. Alistarh et al., 2018]. Another clock type introduced recently in [L. Gąsieniec et al., 2021] enables counting Θ(nlog n) parallel time utilising a fixed number of states and either leaders or connections in the network constructor model. We also discuss parallel efficiency of population protocols referring to protocols operating in Θ(polylog n) parallel time, we propose extensions of the population protocol model leading to further improvement in state and time utilisation, and we state some open problems.
Cite as

Leszek Gąsieniec and Grzegorz Stachowiak. Time, Clocks and Efficiency of Population Protocols (Invited Paper). In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gasieniec_et_al:LIPIcs.SWAT.2022.2,
  author =	{G\k{a}sieniec, Leszek and Stachowiak, Grzegorz},
  title =	{{Time, Clocks and Efficiency of Population Protocols}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{2:1--2:2},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.2},
  URN =		{urn:nbn:de:0030-drops-161624},
  doi =		{10.4230/LIPIcs.SWAT.2022.2},
  annote =	{Keywords: Population protocols, phase clocks, oscillators, parallel time and efficiency}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2018.44
Brief Announcement: Deterministic Contention Resolution on a Shared Channel

Authors: Gianluca De Marco, Dariusz R. Kowalski, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract
A shared channel, also called multiple-access channel, is one of the fundamental communication models. Autonomous entities communicate over a shared medium, and one of the main challenges is how to efficiently resolve collisions occurring when more than one entity attempts to access the channel at the same time. In this work we explore the impact of asynchrony, knowledge (or linear estimate) of the number of contenders, and acknowledgments, on both latency and channel utilization for the Contention resolution problem with non-adaptive deterministic algorithms.
Cite as

Gianluca De Marco, Dariusz R. Kowalski, and Grzegorz Stachowiak. Brief Announcement: Deterministic Contention Resolution on a Shared Channel. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 44:1-44:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{demarco_et_al:LIPIcs.DISC.2018.44,
  author =	{De Marco, Gianluca and Kowalski, Dariusz R. and Stachowiak, Grzegorz},
  title =	{{Brief Announcement: Deterministic Contention Resolution on a Shared Channel}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{44:1--44:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.44},
  URN =		{urn:nbn:de:0030-drops-98331},
  doi =		{10.4230/LIPIcs.DISC.2018.44},
  annote =	{Keywords: Shared channel, multiple-access channel, distributed algorithm}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2016.14
Deterministic Population Protocols for Exact Majority and Plurality

Authors: Leszek Gasieniec, David Hamilton, Russell Martin, Paul G. Spirakis, and Grzegorz Stachowiak

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Abstract
In this paper we study space-efficient deterministic population protocols for several variants of the majority problem including plurality consensus. We focus on space efficient majority protocols in populations with an arbitrary number of colours C represented by k-bit labels, where k = ceiling (log C). In particular, we present asymptotically space-optimal (with respect to the adopted k-bit representation of colours) protocols for (1) the absolute majority problem, i.e., a protocol which decides whether a single colour dominates all other colours considered together, and (2) the relative majority problem, also known in the literature as plurality consensus, in which colours declare their volume superiority versus other individual colours. The new population protocols proposed in this paper rely on a dynamic formulation of the majority problem in which the colours originally present in the population can be changed by an external force during the communication process. The considered dynamic formulation is based on the concepts studied by D. Angluin et al. and O. Michail et al. about stabilizing inputs and composition of population protocols. Also, the protocols presented in this paper use a composition of some known protocols for static and dynamic majority.
Cite as

Leszek Gasieniec, David Hamilton, Russell Martin, Paul G. Spirakis, and Grzegorz Stachowiak. Deterministic Population Protocols for Exact Majority and Plurality. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gasieniec_et_al:LIPIcs.OPODIS.2016.14,
  author =	{Gasieniec, Leszek and Hamilton, David and Martin, Russell and Spirakis, Paul G. and Stachowiak, Grzegorz},
  title =	{{Deterministic Population Protocols for Exact Majority and Plurality}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.14},
  URN =		{urn:nbn:de:0030-drops-70837},
  doi =		{10.4230/LIPIcs.OPODIS.2016.14},
  annote =	{Keywords: Deterministic population protocols, majority, plurality consenus}
}
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