Minimizing broadcast costs under edge reductions in tree networks

We study the broadcasting of messages in the single-port, blocking communication model under edge reductions. Edge reductions model the decrease or elimination of broadcast costs on edges. Let T be an n-vertex tree and B be a target broadcast cost. We present an O(n) time algorithm for determining which edges to reduce (i.e., assign cost 0) such that the number of reduced edges is a minimum and a broadcast initiated at a vertex in a determined center set costs at most B. We present an O(n log n) time algorithm to minimize the cost of a broadcast initiated at an arbitrary vertex