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Near-Optimal Schedules for Simultaneous Multicasts

Authors Bernhard Haeupler, D. Ellis Hershkowitz, David Wajc

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Author Details

Bernhard Haeupler
  • Carnegie Mellon University, Pittsburgh, PA, USA
  • ETH Zürich, Switzerland
D. Ellis Hershkowitz
  • Carnegie Mellon University, Pittsburgh, PA, USA
David Wajc
  • Stanford University, CA, USA

Funding

Supported in part by NSF grants CCF-1527110, CCF-1618280, CCF-1814603, CCF-1910588, NSF CAREER award CCF-1750808, a Sloan Research Fellowship, and funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC grant agreement 949272).
  • Hershkowitz, D. Ellis: Supported by the Air Force Office of Scientific Research under award number FA9550-20-1-0080.
  • Wajc, David: Supported by NSF award 1812919, ONR award N000141912550, and a gift from Cisco Research.

Cite As Get BibTex

Bernhard Haeupler, D. Ellis Hershkowitz, and David Wajc. Near-Optimal Schedules for Simultaneous Multicasts. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 78:1-78:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.78

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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Routing and network design problems
Keywords
  • Packet routing
  • multicast
  • scheduling algorithms

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