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Broadcasting Spanning Forests on a Multiple-Access Channel

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Abstract

The problem of finding a spanning forest of a graph in a distributed-processing environment is studied. If an input graph is weighted, then the goal is to find a minimum-weight spanning forest. The processors communicate by broadcasting. The output consists of the edges that make a spanning forest and have been broadcast on the network. Input edges are distributed among the processors, with each edge held by one processor. The underlying broadcast network is implemented as a multiple-access channel. If exactly one processor attempts to perform a broadcast, then the broadcast is successful. A message broadcast successfully is delivered to all the processors in one step. If more than one processors broadcast simultaneously, then the messages interfere with each other and no processor can receive any of them. Optimality of algorithmic solutions is investigated, by way of comparing deterministic with randomized algorithms, and adaptive with oblivious ones. Lower bounds are proved that either justify the optimality of specific algorithms or show that the optimal performance depends on a class of algorithms.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Colorado at Denver, Campus Box 109, P.O. Box 173364, Denver, CO 80217, USA

    Bogdan S. Chlebus

  2. Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, Warszawa 02-097, Poland

    Bogdan S. Chlebus, Karol Golab & Dariusz R. Kowalski

Authors
  1. Bogdan S. Chlebus
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  2. Karol Golab
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  3. Dariusz R. Kowalski
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Corresponding authors

Correspondence to Bogdan S. Chlebus, Karol Golab or Dariusz R. Kowalski.

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Chlebus, B., Golab, K. & Kowalski, D. Broadcasting Spanning Forests on a Multiple-Access Channel. Theory Comput Systems 36, 711–733 (2003). https://doi.org/10.1007/s00224-003-1149-8

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  • DOI: https://doi.org/10.1007/s00224-003-1149-8

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