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Documents authored by Davies, Peter

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.46
Optimal (Degree+1)-Coloring in Congested Clique

Authors: Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node u of degree d(u) is assigned a palette of d(u)+1 colors, and the goal is to find a proper coloring using these color palettes. The (degree+1)-list coloring problem is a natural generalization of the classical (Δ+1)-coloring and (Δ+1)-list coloring problems, both being benchmark problems extensively studied in distributed and parallel computing. In this paper we settle the complexity of the (degree+1)-list coloring problem in the Congested Clique model by showing that it can be solved deterministically in a constant number of rounds.
Cite as

Sam Coy, Artur Czumaj, Peter Davies, and Gopinath Mishra. Optimal (Degree+1)-Coloring in Congested Clique. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{coy_et_al:LIPIcs.ICALP.2023.46,
  author =	{Coy, Sam and Czumaj, Artur and Davies, Peter and Mishra, Gopinath},
  title =	{{Optimal (Degree+1)-Coloring in Congested Clique}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.46},
  URN =		{urn:nbn:de:0030-drops-180987},
  doi =		{10.4230/LIPIcs.ICALP.2023.46},
  annote =	{Keywords: Distributed computing, graph coloring, parallel computing}
}
Document
DOI: 10.4230/LIPIcs.DISC.2018.15
Deterministic Blind Radio Networks

Authors: Artur Czumaj and Peter Davies

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

Abstract
Ad-hoc radio networks and multiple access channels are classical and well-studied models of distributed systems, with a large body of literature on deterministic algorithms for fundamental communications primitives such as broadcasting and wake-up. However, almost all of these algorithms assume knowledge of the number of participating nodes and the range of possible IDs, and often make the further assumption that the latter is linear in the former. These are very strong assumptions for models which were designed to capture networks of weak devices organized in an ad-hoc manner. It was believed that without this knowledge, deterministic algorithms must necessarily be much less efficient. In this paper we address this fundamental question and show that this is not the case. We present deterministic algorithms for blind networks (in which nodes know only their own IDs), which match or nearly match the running times of the fastest algorithms which assume network knowledge (and even surpass the previous fastest algorithms which assume parameter knowledge but not small labels). Specifically, in multiple access channels with k participating nodes and IDs up to L, we give a wake-up algorithm requiring O((k log L log k)/(log log k)) time, improving dramatically over the O(L^3 log^3 L) time algorithm of De Marco et al. (2007), and a broadcasting algorithm requiring O(k log L log log k) time, improving over the O(L) time algorithm of Gasieniec et al. (2001) in most circumstances. Furthermore, we show how these same algorithms apply directly to multi-hop radio networks, achieving even larger running time improvements.
Cite as

Artur Czumaj and Peter Davies. Deterministic Blind Radio Networks. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czumaj_et_al:LIPIcs.DISC.2018.15,
  author =	{Czumaj, Artur and Davies, Peter},
  title =	{{Deterministic Blind Radio Networks}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{15:1--15:17},
  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.2018.15},
  URN =		{urn:nbn:de:0030-drops-98047},
  doi =		{10.4230/LIPIcs.DISC.2018.15},
  annote =	{Keywords: Broadcasting, Deterministic Algorithms, Radio Networks}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2018.43
Brief Announcement: Randomized Blind Radio Networks

Authors: Artur Czumaj and Peter Davies

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

Abstract
Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. Much work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network n, and the diameter D), which may not be realistic in systems with weak devices or gradual deployment. Little is known about what can be done without this information. This is the issue we address in this work, by presenting the first randomized broadcasting algorithms for blind networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in O(D log n/D log^2 log n/D + log^2 n) time, almost reaching the Omega(D log n/D + log^2 n) lower bound. We also give an even faster algorithm for directed networks with collision detection.
Cite as

Artur Czumaj and Peter Davies. Brief Announcement: Randomized Blind Radio Networks. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czumaj_et_al:LIPIcs.DISC.2018.43,
  author =	{Czumaj, Artur and Davies, Peter},
  title =	{{Brief Announcement: Randomized Blind Radio Networks}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{43:1--43:3},
  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.2018.43},
  URN =		{urn:nbn:de:0030-drops-98323},
  doi =		{10.4230/LIPIcs.DISC.2018.43},
  annote =	{Keywords: Broadcasting, Randomized Algorithms, Radio Networks}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2015.30
Communicating with Beeps

Authors: Artur Czumaj and Peter Davies

Published in: LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

Abstract
The beep model is a very weak communications model in which devices in a network can communicate only via beeps and silence. As a result of its weak assumptions, it has broad applicability to many different implementations of communications networks. This comes at the cost of a restrictive environment for algorithm design. Despite being only recently introduced, the beep model has received considerable attention, in part due to its relationship with other communication models such as that of ad-hoc radio networks. However, there has been no definitive published result for several fundamental tasks in the model. We aim to rectify this with our paper. We present algorithms for the tasks of broadcast, gossiping, and multi-broadcast, and also, as intermediary results, means of depth-first search and diameter estimation. Our O(D+log(M)-time algorithm for broadcasting is a simple formalization of a concept known as beep waves, and is asymptotically optimal. We give an O(n*log(L))-time depth-first search procedure, and show how this can be used as the basis for an O(n*log(L*M))-time gossiping algorithm. Finally, we approach the more general problem of multi-broadcast. We differentiate between two variants of this problem: one where nodes must know the origin of all source messages, and another where this information is not required. In the first instance we achieve an algorithm running in time O(k*log((L*M)/k)+D*log(L)), and in the second an O(k*log(M/k)+D*log(L))-time algorithm (or O(M+D*log(L)) when M <= k). We then give corresponding lower bounds: Omega(k*log((L*M)/k)+D) in the case where nodes must know message origins, and Omega(k*log(M/k)+D) and Omega(M+D) in the other case, for M > k and M <= k respectively. These lower bounds demonstrate that our algorithms are optimal except for the D*log(L) additive term. In these running-time expressions, n represents network size, D network diameter, L range of node labels, M range of source messages, and k number of sources. Our algorithms are all explicit, deterministic, and practical, and give efficient means of communication while making arguably the minimum possible assumptions about the network.
Cite as

Artur Czumaj and Peter Davies. Communicating with Beeps. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{czumaj_et_al:LIPIcs.OPODIS.2015.30,
  author =	{Czumaj, Artur and Davies, Peter},
  title =	{{Communicating with Beeps}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.30},
  URN =		{urn:nbn:de:0030-drops-66195},
  doi =		{10.4230/LIPIcs.OPODIS.2015.30},
  annote =	{Keywords: Beep model, Communication networks, Broadcasting, Gossiping, Leader election}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.139
Faster Deterministic Communication in Radio Networks

Authors: Artur Czumaj and Peter Davies

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad-hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network n, the maximum in-degree of any node Delta, and the eccentricity of the network D. For such networks, we first give an algorithm for wake-up, in both directed and undirected networks, based on the existence of small universal synchronizers. This algorithm runs in O((min{n,D*Delta}*log(n)*log(Delta))/(log(log(Delta)))) time, improving over the previous best O(n*log^2(n))-time result across all ranges of parameters, but particularly when maximum in-degree is small. Next, we introduce a new combinatorial framework of block synchronizers and prove the existence of such objects of low size. Using this framework, we design a new deterministic algorithm for the fundamental problem of broadcasting, running in O(n*log(D)*log(log((D*Delta)/n))) time. This is the fastest known algorithm for this problems, improving upon the O(n*log(n)*log*log(n))-time algorithm of De Marco (2010) and the O(n*log^2(D))-time algorithm due to Czumaj and Rytter (2003), the previous fastest results for directed networks, and is the first to come within a log-logarithmic factor of the Omega(n*log(D)) lower bound due to Clementi et al. (2003). Our results have also direct implications on the fastest deterministic leader election and clock synchronization algorithms in both directed and undirected radio networks, tasks which are commonly used as building blocks for more complex procedures.
Cite as

Artur Czumaj and Peter Davies. Faster Deterministic Communication in Radio Networks. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 139:1-139:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2016.139,
  author =	{Czumaj, Artur and Davies, Peter},
  title =	{{Faster Deterministic Communication in Radio Networks}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{139:1--139:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.139},
  URN =		{urn:nbn:de:0030-drops-62838},
  doi =		{10.4230/LIPIcs.ICALP.2016.139},
  annote =	{Keywords: Radio networks, Communication networks, Broadcasting, Wake-Up, Deterministic algorithms}
}
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