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The Telephone k-Multicast Problem

Authors Daniel Hathcock , Guy Kortsarz, R. Ravi

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Author Details

Daniel Hathcock
  • Carnegie Mellon University, United States
Guy Kortsarz
  • Rutgers University, Camden, United States
R. Ravi
  • Carnegie Mellon University, United States

Funding

  • Hathcock, Daniel: Supported by the NSF Graduate Research Fellowship grant DGE-2140739
  • Ravi, R.: This material is based upon work supported in part by the Air Force Office of Scientific Research under award number FA9550-23-1-0031 to RR.

Cite AsGet BibTex

Daniel Hathcock, Guy Kortsarz, and R. Ravi. The Telephone k-Multicast Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.21

Abstract

We consider minimum time multicasting problems in directed and undirected graphs: given a root node and a subset of t terminal nodes, multicasting seeks to find the minimum number of rounds within which all terminals can be informed with a message originating at the root. In each round, the telephone model we study allows the information to move via a matching from the informed nodes to the uninformed nodes. Since minimum time multicasting in digraphs is poorly understood compared to the undirected variant, we study an intermediate problem in undirected graphs that specifies a target k < t, and requires the only k of the terminals be informed in the minimum number of rounds. For this problem, we improve implications of prior results and obtain an Õ(t^{1/3}) multiplicative approximation. For the directed version, we obtain an additive Õ(k^{1/2}) approximation algorithm (with a poly-logarithmic multiplicative factor). Our algorithms are based on reductions to the related problems of finding k-trees of minimum poise (sum of maximum degree and diameter) and applying a combination of greedy network decomposition techniques and set covering under partition matroid constraints.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Network Design
  • Multicast
  • Steiner Poise

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References

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