Optimal linear broadcast routing with capacity limitations

Abstract

We study the problem of broadcast routing in high-speed networks with special switching hardware. In such networks replication of a packet in each internal vertex (as done in traditional broadcast algorithms) is inefficient. The method that is used in such networks is linear broadcast routing, in which the packets travel along linear routes, determined in the header of the packet. In this routing several packets travel simultaneously through one communication line and one switching subsystem. Each edge has a communication cost, and the total cost of the routing is determined by either the number of the packets or by the total cost of edges traversed.

The problem that arises in realistic networks is that of linear broadcast routing with limited bandwidth, that corresponds to edge capacity in the underlying graph. We show that the problem of determining the linear broadcast routing, with either smallest number of packets or with the smallest cost of edges utilization (for a given number of packets), for either bounded or unbounded headers, and with capacity limitations, is NP-hard for general graphs. We present polynomial-time algorithms for tree networks, for all of the above cases, in which the header is unbounded.