Computing global combine operations in the multi-port postal model

Abstract

Abstract-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 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 multiport postal model. 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 from k other processors 1 -1 rounds earlier. This paper provides an optimal algorithm for the global combine problem that requires the least number of communication rounds and minimizes the time spent by any processor in sending and receiving messages.

Fast collective communication by packets in the postal model

“…As in previous papers dealing with the computation of global clic Resolution [10,13]. Both operations have been included in the Message-Passing Interface standard profunctions in the postal model, we assume that the communication latency is an integer l ¢ 1 [3,5,6]. When posal [31] and are part of various software platforms including CCL [2], PVM [19], and Express [30].…”

“…The multiport model has been extensively sage. considered in the literature (see the survey [21]); the first paper to combine both the multiport and the postal model into one model is [3]. The m-port postal model considers…”

Optimal software multicast in wormhole-routed multistage networks

“…In [4], an optimal unicast-based multicast algorithm is developed for direct networks characterized by multi-dimensional mesh topology and oneport communication architecture. Recently, several algorithms [5,6,7] are proposed for efficient unicastbased implementation of collective communication services in direct networks which support all-port communication. Among them, an optimal unicast-based broadcast algorithm [7] is achieved for hypercube networks.…”

A linear algorithm for finding the k‐broadcast center of a tree

“…This model allows for "conference calls" of a limited maximum size k [10]. It is useful in the study of DMA-bound systems [23] and also has application in computing functions in networks [1,3,5].…”