Communication complexity of gossiping by packets

Abstract

This paper considers the problem of gossiping with packets of limited size in a network with cost function. We show that the problem of determining the minimum cost necessary to perform gossiping among a given set of participants with packets of limited size is NP-hard. We also give an approximate (with respect to the cost) gossiping algorithm. The ratio between the cost of an optimal algorithm and the approximate one is less than 1+2(k-1)/n, were n is the number of nodes participating to the gossiping process and k < n - 1 is the upper bound on the number of individual blocks of information that a packet can carry. We also analyze the communication time and communication complexity, i.e., the product of the communication cost and time, of goSsiping algorithms.