Search Results

Documents authored by Izumi, Taisuke


Document
Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs

Authors: Taichi Inoue, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa

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


Abstract
We investigated the computational power of a single mobile agent in an n-node graph with storage (i.e., node memory). Generally, a system with one-bit agent memory and O(1)-bit storage is as powerful as that with O(n)-bit agent memory and O(1)-bit storage. Thus, we focus on the difference between one-bit memory and oblivious (i.e., zero-bit memory) agents. Although their computational powers are not equivalent, all the known results exhibiting such a difference rely on the fact that oblivious agents cannot transfer any information from one side to the other across the bridge edge. Hence, our main question is as follows: Are the computational powers of one-bit memory and oblivious agents equivalent in 2-edge-connected graphs or not? The main contribution of this study is to answer this question under the relaxed assumption that each node has O(logΔ)-bit storage (where Δ is the maximum degree of the graph). We present an algorithm for simulating any algorithm for a single one-bit memory agent using an oblivious agent with O(n²)-time overhead per round. Our results imply that the topological structure of graphs differentiating the computational powers of oblivious and non-oblivious agents is completely characterized by the existence of bridge edges.

Cite as

Taichi Inoue, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa. Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 11:1-11:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{inoue_et_al:LIPIcs.OPODIS.2022.11,
  author =	{Inoue, Taichi and Kitamura, Naoki and Izumi, Taisuke and Masuzawa, Toshimitsu},
  title =	{{Computational Power of a Single Oblivious Mobile Agent in Two-Edge-Connected Graphs}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{11:1--11:18},
  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.2022.11},
  URN =		{urn:nbn:de:0030-drops-176311},
  doi =		{10.4230/LIPIcs.OPODIS.2022.11},
  annote =	{Keywords: mobile agent, depth-first search, space complexity}
}
Document
Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols

Authors: Yuichi Sudo, Ryota Eguchi, Taisuke Izumi, and Toshimitsu Masuzawa

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)


Abstract
We consider the leader election problem in the population protocol model. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e., the knowledge of the exact size of a network) and rich computational resource (i.e., the number of states). Loose-stabilization is a promising relaxed concept of self-stabilization to address the aforementioned issue. Loose-stabilization guarantees that starting from any configuration, the network will reach a safe configuration where a single leader exists within a short time, and thereafter it will maintain the single leader for a long time, but not necessarily forever. The main contribution of this paper is giving a time-optimal loosely-stabilizing leader election protocol. The proposed protocol with design parameter τ ≥ 1 attains O(τ log n) parallel convergence time and Ω(n^τ) parallel holding time (i.e., the length of the period keeping the unique leader), both in expectation. This protocol is time-optimal in the sense of both the convergence and holding times in expectation because any loosely-stabilizing leader election protocol with the same length of the holding time is known to require Ω(τ log n) parallel time.

Cite as

Yuichi Sudo, Ryota Eguchi, Taisuke Izumi, and Toshimitsu Masuzawa. Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 40:1-40:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{sudo_et_al:LIPIcs.DISC.2021.40,
  author =	{Sudo, Yuichi and Eguchi, Ryota and Izumi, Taisuke and Masuzawa, Toshimitsu},
  title =	{{Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.40},
  URN =		{urn:nbn:de:0030-drops-148427},
  doi =		{10.4230/LIPIcs.DISC.2021.40},
  annote =	{Keywords: population protocols, leader election, loose-stabilization, self-stabilization}
}
Document
Track A: Algorithms, Complexity and Games
Sublinear-Space Lexicographic Depth-First Search for Bounded Treewidth Graphs and Planar Graphs

Authors: Taisuke Izumi and Yota Otachi

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)


Abstract
The lexicographic depth-first search (Lex-DFS) is one of the first basic graph problems studied in the context of space-efficient algorithms. It is shown independently by Asano et al. [ISAAC 2014] and Elmasry et al. [STACS 2015] that Lex-DFS admits polynomial-time algorithms that run with O(n)-bit working memory, where n is the number of vertices in the graph. Lex-DFS is known to be P-complete under logspace reduction, and giving or ruling out polynomial-time sublinear-space algorithms for Lex-DFS on general graphs is quite challenging. In this paper, we study Lex-DFS on graphs of bounded treewidth. We first show that given a tree decomposition of width O(n^(1-ε)) with ε > 0, Lex-DFS can be solved in sublinear space. We then complement this result by presenting a space-efficient algorithm that can compute, for w ≤ √n, a tree decomposition of width O(w √nlog n) or correctly decide that the graph has a treewidth more than w. This algorithm itself would be of independent interest as the first space-efficient algorithm for computing a tree decomposition of moderate (small but non-constant) width. By combining these results, we can show in particular that graphs of treewidth O(n^(1/2 - ε)) for some ε > 0 admits a polynomial-time sublinear-space algorithm for Lex-DFS. We can also show that planar graphs admit a polynomial-time algorithm with O(n^(1/2+ε))-bit working memory for Lex-DFS.

Cite as

Taisuke Izumi and Yota Otachi. Sublinear-Space Lexicographic Depth-First Search for Bounded Treewidth Graphs and Planar Graphs. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 67:1-67:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{izumi_et_al:LIPIcs.ICALP.2020.67,
  author =	{Izumi, Taisuke and Otachi, Yota},
  title =	{{Sublinear-Space Lexicographic Depth-First Search for Bounded Treewidth Graphs and Planar Graphs}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{67:1--67:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.67},
  URN =		{urn:nbn:de:0030-drops-124745},
  doi =		{10.4230/LIPIcs.ICALP.2020.67},
  annote =	{Keywords: depth-first search, space complexity, treewidth}
}
Document
Quantum Distributed Algorithm for Triangle Finding in the CONGEST Model

Authors: Taisuke Izumi, François Le Gall, and Frédéric Magniez

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
This paper considers the triangle finding problem in the CONGEST model of distributed computing. Recent works by Izumi and Le Gall (PODC'17), Chang, Pettie and Zhang (SODA'19) and Chang and Saranurak (PODC'19) have successively reduced the classical round complexity of triangle finding (as well as triangle listing) from the trivial upper bound O(n) to Õ(n^{1/3}), where n denotes the number of vertices in the graph. In this paper we present a quantum distributed algorithm that solves the triangle finding problem in Õ(n^{1/4}) rounds in the CONGEST model. This gives another example of quantum algorithm beating the best known classical algorithms in distributed computing. Our result also exhibits an interesting phenomenon: while in the classical setting the best known upper bounds for the triangle finding and listing problems are identical, in the quantum setting the round complexities of these two problems are now Õ(n^{1/4}) and Θ~(n^{1/3}), respectively. Our result thus shows that triangle finding is easier than triangle listing in the quantum CONGEST model.

Cite as

Taisuke Izumi, François Le Gall, and Frédéric Magniez. Quantum Distributed Algorithm for Triangle Finding in the CONGEST Model. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 23:1-23:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{izumi_et_al:LIPIcs.STACS.2020.23,
  author =	{Izumi, Taisuke and Le Gall, Fran\c{c}ois and Magniez, Fr\'{e}d\'{e}ric},
  title =	{{Quantum Distributed Algorithm for Triangle Finding in the CONGEST Model}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{23:1--23:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.23},
  URN =		{urn:nbn:de:0030-drops-118840},
  doi =		{10.4230/LIPIcs.STACS.2020.23},
  annote =	{Keywords: Quantum computing, distributed computing, CONGEST model}
}
Document
Towards Distributed Two-Stage Stochastic Optimization

Authors: Yuval Emek, Noga Harlev, and Taisuke Izumi

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)


Abstract
The weighted vertex cover problem is concerned with selecting a subset of the vertices that covers a target set of edges with the objective of minimizing the total cost of the selected vertices. We consider a variant of this classic combinatorial optimization problem where the target edge set is not fully known; rather, it is characterized by a probability distribution. Adhering to the model of two-stage stochastic optimization, the execution is divided into two stages so that in the first stage, the decision maker selects some of the vertices based on the probabilistic forecast of the target edge set. Then, in the second stage, the edges in the target set are revealed and in order to cover them, the decision maker can augment the vertex subset selected in the first stage with additional vertices. However, in the second stage, the vertex cost increases by some inflation factor, so the second stage selection becomes more expensive. The current paper studies the two-stage stochastic vertex cover problem in the realm of distributed graph algorithms, where the decision making process (in both stages) is distributed among the vertices of the graph. By combining the stochastic optimization toolbox with recent advances in distributed algorithms for weighted vertex cover, we develop an algorithm that runs in time O(log (Δ) / ε), sends O(m) messages in total, and guarantees to approximate the optimal solution within a (3 + ε)-ratio, where m is the number of edges in the graph, Δ is its maximum degree, and 0 < ε < 1 is a performance parameter.

Cite as

Yuval Emek, Noga Harlev, and Taisuke Izumi. Towards Distributed Two-Stage Stochastic Optimization. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 32:1-32:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{emek_et_al:LIPIcs.OPODIS.2019.32,
  author =	{Emek, Yuval and Harlev, Noga and Izumi, Taisuke},
  title =	{{Towards Distributed Two-Stage Stochastic Optimization}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.32},
  URN =		{urn:nbn:de:0030-drops-118187},
  doi =		{10.4230/LIPIcs.OPODIS.2019.32},
  annote =	{Keywords: weighted vertex cover, distributed graph algorithms, two-stage stochastic optimization, primal-dual}
}
Document
Message Reduction in the LOCAL Model Is a Free Lunch

Authors: Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)


Abstract
A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity.

Cite as

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Message Reduction in the LOCAL Model Is a Free Lunch. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 7:1-7:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bitton_et_al:LIPIcs.DISC.2019.7,
  author =	{Bitton, Shimon and Emek, Yuval and Izumi, Taisuke and Kutten, Shay},
  title =	{{Message Reduction in the LOCAL Model Is a Free Lunch}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.7},
  URN =		{urn:nbn:de:0030-drops-113145},
  doi =		{10.4230/LIPIcs.DISC.2019.7},
  annote =	{Keywords: distributed graph algorithms, spanner, LOCAL model, message complexity}
}
Document
Low-Congestion Shortcut and Graph Parameters

Authors: Naoki Kitamura, Hirotaka Kitagawa, Yota Otachi, and Taisuke Izumi

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)


Abstract
Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Omega~(sqrt{n} + D) rounds for many global problems, where n is the number of nodes and D is the diameter of the input graph. Since such a lower bound is derived from special "hard-core" instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts is initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. Specifically, given a specific graph class X, an f-round algorithm of constructing shortcuts of quality q for any instance in X results in O~(q + f)-round algorithms of solving several fundamental graph problems such as minimum spanning tree and minimum cut, for X. The main interest on this line is to identify the graph classes allowing the shortcuts which are efficient in the sense of breaking O~(sqrt{n}+D)-round general lower bounds. In this paper, we consider the relationship between the quality of low-congestion shortcuts and three major graph parameters, chordality, diameter, and clique-width. The main contribution of the paper is threefold: (1) We show an O(1)-round algorithm which constructs a low-congestion shortcut with quality O(kD) for any k-chordal graph, and prove that the quality and running time of this construction is nearly optimal up to polylogarithmic factors. (2) We present two algorithms, each of which constructs a low-congestion shortcut with quality O~(n^{1/4}) in O~(n^{1/4}) rounds for graphs of D=3, and that with quality O~(n^{1/3}) in O~(n^{1/3}) rounds for graphs of D=4 respectively. These results obviously deduce two MST algorithms running in O~(n^{1/4}) and O~(n^{1/3}) rounds for D=3 and 4 respectively, which almost close the long-standing complexity gap of the MST construction in small-diameter graphs originally posed by Lotker et al. [Distributed Computing 2006]. (3) We show that bounding clique-width does not help the construction of good shortcuts by presenting a network topology of clique-width six where the construction of MST is as expensive as the general case.

Cite as

Naoki Kitamura, Hirotaka Kitagawa, Yota Otachi, and Taisuke Izumi. Low-Congestion Shortcut and Graph Parameters. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 25:1-25:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{kitamura_et_al:LIPIcs.DISC.2019.25,
  author =	{Kitamura, Naoki and Kitagawa, Hirotaka and Otachi, Yota and Izumi, Taisuke},
  title =	{{Low-Congestion Shortcut and Graph Parameters}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.25},
  URN =		{urn:nbn:de:0030-drops-113328},
  doi =		{10.4230/LIPIcs.DISC.2019.25},
  annote =	{Keywords: distributed graph algorithms, low-congestion shortcut, k-chordal graph, clique width, minimum spanning tree}
}
Document
Uniform Distribution On Pachinko

Authors: Naoki Kitamura, Yuya Kawabata, and Taisuke Izumi

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)


Abstract
Pachinko is a japanese mechanical gambling game similar to pinball. Recently, Akitaya et al. proposed several mathematical models of Pachinko. A number of pins are spiked in a field. A ball drops from the top-side end of the playfield, and falls down. In the 50-50 model, if the ball hits a pin, it moves to the left or right of the pin with equal probability. An arrangement of pins generates a distribution of the drop probability over all columns. We consider the problem of generating uniform distributions. Akitaya et al. show that (1/2^{{a}})-uniform distribution is possible for {a} in {0,1,2,3,4} and conjectured that it is possible for any positive integer a. In this paper, we show that the conjecture is true by a constructive way.

Cite as

Naoki Kitamura, Yuya Kawabata, and Taisuke Izumi. Uniform Distribution On Pachinko. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 26:1-26:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{kitamura_et_al:LIPIcs.FUN.2018.26,
  author =	{Kitamura, Naoki and Kawabata, Yuya and Izumi, Taisuke},
  title =	{{Uniform Distribution On Pachinko}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.26},
  URN =		{urn:nbn:de:0030-drops-88170},
  doi =		{10.4230/LIPIcs.FUN.2018.26},
  annote =	{Keywords: Pachinko, discrete mathematics}
}
Document
Brief Announcement
Brief Announcement: Fast Aggregation in Population Protocols

Authors: Ryota Eguchi and Taisuke Izumi

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)


Abstract
The coalescence protocol plays an important role in the population protocol model. The conceptual structure of the protocol is for two agents holding two non-zero values a, b respectively to take a transition (a,b) -> (a+b, 0), where + is an arbitrary commutative binary operation. Obviously, it eventually aggregates the sum of all initial values. In this paper, we present a fast coalescence protocol that converges in O(sqrt(n) log^2 n) parallel time with high probability in the model with an initial leader (equivalently, the model with a base station), which achieves an substantial speed-up compared with the naive implementation taking Omega(n) time.

Cite as

Ryota Eguchi and Taisuke Izumi. Brief Announcement: Fast Aggregation in Population Protocols. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 49:1-49:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{eguchi_et_al:LIPIcs.DISC.2017.49,
  author =	{Eguchi, Ryota and Izumi, Taisuke},
  title =	{{Brief Announcement: Fast Aggregation in Population Protocols}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{49:1--49:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.49},
  URN =		{urn:nbn:de:0030-drops-79981},
  doi =		{10.4230/LIPIcs.DISC.2017.49},
  annote =	{Keywords: population protocol, aggregation}
}
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