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Improved Lower Bound on Broadcast Function Based on Graph Partition

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Combinatorial Algorithms (IWOCA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10765))

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Abstract

Broadcasting is a one-to-all information spreading process in a communication network. The network is modeled as a graph. The broadcast time of a given vertex is the minimum time required to broadcast a message from that vertex to all vertices of the graph. The broadcast time of a graph is the maximum time required to broadcast from any vertex in the graph. A graph G on n vertices is a minimum broadcast graph if the broadcast time of G is the minimum possible time: \(\lceil \log n\rceil \), and the number of edges in G is minimized. The broadcast function B(n) denotes the number of edges in a minimum broadcast graph on n vertices. The exact value of B(n) is only known for \(n=2^m\), \(2^m-2\), and some small values of \(n<64\). Finding B(n) is very difficult due to the lack of tight lower bounds on B(n). The existing lower bounds are based on the vertex degree of the originator vertex. However, most of the minimum broadcast graphs are not necessarily regular. In this paper, we present an improved general lower bound on B(n) based on new observations about partitioning broadcast graphs.

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Authors and Affiliations

  1. Concordia University, Montreal, QC, H3G 1M8, Canada

    Hovhannes A. Harutyunyan & Zhiyuan Li

Authors
  1. Hovhannes A. Harutyunyan
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  2. Zhiyuan Li
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Correspondence to Zhiyuan Li .

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Editors and Affiliations

  1. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Ljiljana Brankovic

  2. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Joe Ryan

  3. McMaster University, Hamilton, Ontario, Canada

    William F. Smyth

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Harutyunyan, H.A., Li, Z. (2018). Improved Lower Bound on Broadcast Function Based on Graph Partition. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_18

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  • DOI: https://doi.org/10.1007/978-3-319-78825-8_18

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  • Print ISBN: 978-3-319-78824-1

  • Online ISBN: 978-3-319-78825-8

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