3 Search Results for "Mashreghi, Ali"

Document
DOI: 10.4230/LIPIcs.OPODIS.2024.26
The Singular Optimality of Distributed Computation in LOCAL

Authors: Fabien Dufoulon, Gopal Pandurangan, Peter Robinson, and Michele Scquizzato

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

Abstract
It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global problems such as broadcast, leader election, and spanning tree construction, under the KT₀ assumption. With this assumption, nodes have initial knowledge only of themselves, not their neighbors. In this case the time and message lower bounds are Ω(D) and Ω(m), respectively, where D is the diameter of the network and m is the number of edges, and there exist (even) deterministic algorithms that simultaneously match these bounds. On the other hand, under the KT₁ assumption, whereby each node has initial knowledge of itself and the identifiers of its neighbors, the situation is not clear. For the KT₁ CONGEST model (where messages are of small size), King, Kutten, and Thorup (KKT) showed that one can solve several fundamental global problems (with the notable exception of BFS tree construction) such as broadcast, leader election, and spanning tree construction with Õ(n) message complexity (n is the network size), which can be significantly smaller than m. Randomization is crucial in obtaining this result. While the message complexity of the KKT result is near-optimal, its time complexity is Õ(n) rounds, which is far from the standard lower bound of Ω(D). An important open question is whether one can achieve singular optimality for the above problems in the KT₁ CONGEST model, i.e., whether there exists an algorithm running in Õ(D) rounds and Õ(n) messages. Another important and related question is whether the fundamental BFS tree construction can be solved with Õ(n) messages (regardless of the number of rounds as long as it is polynomial in n) in KT₁. In this paper, we show that in the KT₁ LOCAL model (where message sizes are not restricted), singular optimality is achievable. Our main result is that all global problems, including BFS tree construction, can be solved in Õ(D) rounds and Õ(n) messages, where both bounds are optimal up to polylogarithmic factors. Moreover, we show that this can be achieved deterministically.
Cite as

Fabien Dufoulon, Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. The Singular Optimality of Distributed Computation in LOCAL. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dufoulon_et_al:LIPIcs.OPODIS.2024.26,
  author =	{Dufoulon, Fabien and Pandurangan, Gopal and Robinson, Peter and Scquizzato, Michele},
  title =	{{The Singular Optimality of Distributed Computation in LOCAL}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{26:1--26:17},
  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.2024.26},
  URN =		{urn:nbn:de:0030-drops-225629},
  doi =		{10.4230/LIPIcs.OPODIS.2024.26},
  annote =	{Keywords: Distributed algorithms, round and message complexity, BFS tree construction, leader election}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2019.49
Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication

Authors: Ali Mashreghi and Valerie King

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

Abstract
Building a spanning tree, minimum spanning tree (MST), and BFS tree in a distributed network are fundamental problems which are still not fully understood in terms of time and communication cost. The first work to succeed in computing a spanning tree with communication sublinear in the number of edges in an asynchronous CONGEST network appeared in DISC 2018. That algorithm which constructs an MST is sequential in the worst case; its running time is proportional to the total number of messages sent. Our paper matches its message complexity but brings the running time down to linear in n. Our techniques can also be used to provide an asynchronous algorithm with sublinear communication to construct a tree in which the distance from a source to each node is within an additive term of sqrt{n} of its actual distance.
Cite as

Ali Mashreghi and Valerie King. Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 49:1-49:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mashreghi_et_al:LIPIcs.DISC.2019.49,
  author =	{Mashreghi, Ali and King, Valerie},
  title =	{{Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{49:1--49:3},
  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.2019.49},
  URN =		{urn:nbn:de:0030-drops-113566},
  doi =		{10.4230/LIPIcs.DISC.2019.49},
  annote =	{Keywords: Distributed Computing, Minimum Spanning Tree, Broadcast Tree}
}
Document
DOI: 10.4230/LIPIcs.DISC.2018.37
Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model

Authors: Ali Mashreghi and Valerie King

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

Abstract
We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o(m) bits of communication, in a sufficiently dense graph with n nodes and m edges. For decades, it was believed that Omega(m) bits of communication are required for any algorithm that constructs a broadcast tree. In 2015, King, Kutten and Thorup showed that in the KT1 model where nodes have initial knowledge of their neighbors' identities it is possible to construct MST in O~(n) messages in the synchronous CONGEST model. In the CONGEST model messages are of size O(log n). However, no algorithm with o(m) messages were known for the asynchronous case. Here, we provide an algorithm that uses O(n^{3/2} log^{3/2} n) messages to find MST in the asynchronous CONGEST model. Our algorithm is randomized Monte Carlo and outputs MST with high probability. We will provide an algorithm for computing a spanning tree with O(n^{3/2} log^{3/2} n) messages. Given a spanning tree, we can compute MST with O~(n) messages.
Cite as

Ali Mashreghi and Valerie King. Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{mashreghi_et_al:LIPIcs.DISC.2018.37,
  author =	{Mashreghi, Ali and King, Valerie},
  title =	{{Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{37:1--37:17},
  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.2018.37},
  URN =		{urn:nbn:de:0030-drops-98263},
  doi =		{10.4230/LIPIcs.DISC.2018.37},
  annote =	{Keywords: Distributed Computing, Minimum Spanning Tree, Broadcast Tree}
}
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