Extending the birkhoff-von neumann switching strategy to multicast switches

Authors:
Jay Kumar Sundararajan;Supratim Deb;Muriel Médard
Affiliations:
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology;Laboratory for Information and Decision Systems, Massachusetts Institute of Technology;Laboratory for Information and Decision Systems, Massachusetts Institute of Technology
Venue:
NETWORKING'05 Proceedings of the 4th IFIP-TC6 international conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communication Systems
Year:
2005

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Abstract

This paper extends the Birkhoff-von Neumann unicast switching strategy to the multicast case. Using a graph theoretic model we show that the rate region for a traffic pattern is precisely the stable set polytope of the pattern's ‘conflict graph', in the no-fanout splitting case. Computing the offline schedule is equivalent to fractional weighted graph coloring which takes polynomial time for perfect graphs. For a general conflict graph, we show that deciding achievability of a given rate vector is NP-hard, but can be done in polynomial time for the case of moderate multicast load. The result naturally leads to an offline schedule.