Computing Global Combine Operations in the Multi-Port Postal Model

Consider a message-passing system of n processors, in which each processor holds one piece of data initially. The goal is to compute an associative and commutative reduction function on the n distributed pieces of data and to make the result known to all the n processors. This operation is frequently used in many message-passing systems and is typically referred to as global combine, census computation, or gossiping. This paper explores the problem of global combine in the multi-port postal model for message-passing systems. This model is characterized by three parameters: n --- the number of processors, k --- the number of ports per processor, and --- the communication latency. In this model, in every round r, each processor can send k distinct messages to k other processors, and it can receive k messages that were sent out from k other processors \Gamma 1 rounds earlier. This paper provides an optimal algorithm for the global combine problem that requires the least number of comm..