License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.78
URN: urn:nbn:de:0030-drops-141471
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14147/
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Haeupler, Bernhard ; Hershkowitz, D. Ellis ; Wajc, David

Near-Optimal Schedules for Simultaneous Multicasts

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LIPIcs-ICALP-2021-78.pdf (0.8 MB)

Abstract

We study the store-and-forward packet routing problem for simultaneous multicasts, in which multiple packets have to be forwarded along given trees as fast as possible.
This is a natural generalization of the seminal work of Leighton, Maggs and Rao, which solved this problem for unicasts, i.e. the case where all trees are paths. They showed the existence of asymptotically optimal O(C + D)-length schedules, where the congestion C is the maximum number of packets sent over an edge and the dilation D is the maximum depth of a tree. This improves over the trivial O(CD) length schedules.
We prove a lower bound for multicasts, which shows that there do not always exist schedules of non-trivial length, o(CD). On the positive side, we construct O(C+D+log² n)-length schedules in any n-node network. These schedules are near-optimal, since our lower bound shows that this length cannot be improved to O(C+D) + o(log n).

BibTeX - Entry

@InProceedings{haeupler_et_al:LIPIcs.ICALP.2021.78,
  author =	{Haeupler, Bernhard and Hershkowitz, D. Ellis and Wajc, David},
  title =	{{Near-Optimal Schedules for Simultaneous Multicasts}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{78:1--78:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14147},
  URN =		{urn:nbn:de:0030-drops-141471},
  doi =		{10.4230/LIPIcs.ICALP.2021.78},
  annote =	{Keywords: Packet routing, multicast, scheduling algorithms}
}

Keywords: Packet routing, multicast, scheduling algorithms
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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