Abstract
This paper addresses the minimum-time broadcast problem under several modes of the line model, i.e., when long-distance calls can be placed along paths in the network. It is well known that the minimum-time broadcast problem can be solved in polynomial time under the single-port edge-disjoint paths mode. However, it is equally well known that either relaxing the model to the all-port edge-disjoint paths mode, or constraining the model to the single-port vertex-disjoint paths mode, leads to NP-complete problems; and exact solutions have been derived for specific topologies only (e.g., hypercubes or tori). In this paper we present polynomial-time algorithms for minimum-time broadcast in trees. These algorithms are obtained by application of an original technique called the merging method , which can be applied in a larger context, for instance, to solve the multicast problem or to address the restricted regimen. The merging method requires solving the minimal contention-free matrix problem whose solution presents some interest on its own.
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Cohen, Fraigniaud & Mitjana Polynomial-Time Algorithms for Minimum-Time Broadcast in Trees . Theory Comput. Systems 35, 641–665 (2002). https://doi.org/10.1007/s00224-002-1047-5
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DOI: https://doi.org/10.1007/s00224-002-1047-5