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DOI: 10.4230/LIPIcs.ESA.2019.78

Multicommodity Multicast, Wireless and Fast

Authors: R. Ravi and Oleksandr Rudenko

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract

We study rumor spreading in graphs, specifically multicommodity multicast problem under the wireless model: given source-destination pairs in the graph, one needs to find the fastest schedule to transfer information from each source to the corresponding destination. Under the wireless model, nodes can transmit to any subset of their neighbors in synchronous time steps, as long as they either transmit or receive from at most one transmitter during the same time step. We improve approximation ratio for this problem from O~(n^(2/3)) to O~(n^((1/2) + epsilon)) on n-node graphs. We also design an algorithm that satisfies p given demand pairs in O(OPT + p) steps, where OPT is the length of an optimal schedule, by reducing it to the well-studied packet routing problem. In the case where underlying graph is an n-node tree, we improve the previously best-known approximation ratio of O((log n)/(log log n)) to 3. One consequence of our proof is a simple constructive rule for optimal broadcasting in a tree under a widely studied telephone model.

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R. Ravi and Oleksandr Rudenko. Multicommodity Multicast, Wireless and Fast. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ravi_et_al:LIPIcs.ESA.2019.78,
  author =	{Ravi, R. and Rudenko, Oleksandr},
  title =	{{Multicommodity Multicast, Wireless and Fast}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{78:1--78:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.78},
  URN =		{urn:nbn:de:0030-drops-111991},
  doi =		{10.4230/LIPIcs.ESA.2019.78},
  annote =	{Keywords: Rumor, scheduling, broadcast, multicommodity, multicast, optimization algorithms, approximation, packet routing}
}

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Multicommodity Multicast, Wireless and Fast

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