DROPS

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DOI: 10.4230/LIPIcs.OPODIS.2023.22

Local Recurrent Problems in the SUPPORTED Model

Authors: Akanksha Agrawal, John Augustine, David Peleg, and Srikkanth Ramachandran

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract

We study the SUPPORTED model of distributed computing introduced by Schmid and Suomela [Schmid and Suomela, 2013], which generalizes the LOCAL and CONGEST models. In this framework, multiple instances of the same problem, differing from each other by the subnetwork to which they apply. recur over time, and need to be solved efficiently online. To do that, one may rely on an initial preprocessing phase for computing some useful information. This preprocessing phase makes it possible, in some cases, to obtain improved distributed algorithms, overcoming locality-based time lower bounds. Our main contribution is to expand the class of problems to which the SUPPORTED model applies, by handling also multiple recurring instances of the same problem that differ from each other by some problem specific input, and not only the subnetwork to which they apply. We illustrate this by considering two extended problem classes. The first class, denoted PCS, concerns problems where client nodes of the network need to be served, and each recurring instance applies to some Partial Client Set. The second class, denoted PFO, concerns situations where each recurrent instance of the problem includes a partially fixed output, which needs to be completed to a full consistent solution. Specifically, we propose some natural recurrent variants of the dominating set problem and the coloring problem that are of interest particularly in the distributed setting. For these problems, we show that information about the topology can be used to overcome locality-based lower bounds. We also categorize the round complexity of Locally Checkable Labellings in the SUPPORTED model for the simple case of paths. Finally we present some interesting open problems and some partial results towards resolving them.

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Akanksha Agrawal, John Augustine, David Peleg, and Srikkanth Ramachandran. Local Recurrent Problems in the SUPPORTED Model. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{agrawal_et_al:LIPIcs.OPODIS.2023.22,
  author =	{Agrawal, Akanksha and Augustine, John and Peleg, David and Ramachandran, Srikkanth},
  title =	{{Local Recurrent Problems in the SUPPORTED Model}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.22},
  URN =		{urn:nbn:de:0030-drops-195124},
  doi =		{10.4230/LIPIcs.OPODIS.2023.22},
  annote =	{Keywords: Distributed Algorithms, LOCAL Model, SUPPORTED Model}
}

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Brief Announcement

DOI: 10.4230/LIPIcs.SAND.2022.21

Brief Announcement: Cooperative Guarding in Polygons with Holes

Authors: John Augustine and Srikkanth Ramachandran

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract

We study the Cooperative Guarding problem for polygons with holes in a mobile multi-agents setting. Given a set of agents, initially deployed at a point in a polygon with n vertices and h holes, we require the agents to collaboratively explore and position themselves in such a way that every point in the polygon is visible to at least one agent and that the set of agents are visibly connected. We study the problem under two models of computation, one in which the agents can compute exact distances and angles between two points in its visibility, and one in which agents can only compare distances and angles. In the stronger model, we provide a deterministic O(n) round algorithm to compute such a cooperative guard set while not requiring more than (n + h)/2 agents and O(log n) bits of persistent memory per agent. In the weaker model, we provide an O(n⁴) round algorithm, that does not require more than (n+2h)/2 agents.

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John Augustine and Srikkanth Ramachandran. Brief Announcement: Cooperative Guarding in Polygons with Holes. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 21:1-21:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{augustine_et_al:LIPIcs.SAND.2022.21,
  author =	{Augustine, John and Ramachandran, Srikkanth},
  title =	{{Brief Announcement: Cooperative Guarding in Polygons with Holes}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{21:1--21:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.21},
  URN =		{urn:nbn:de:0030-drops-159636},
  doi =		{10.4230/LIPIcs.SAND.2022.21},
  annote =	{Keywords: Mobile Agents, Art Gallery Problem, Cooperative Guarding}
}

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Documents authored by Ramachandran, Srikkanth

Local Recurrent Problems in the SUPPORTED Model

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Brief Announcement: Cooperative Guarding in Polygons with Holes

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