Optimal all-to-all personalized communication on Butterfly networks through a reduced Latin square

Izzi, Daniele; Massini, Annalisa

doi:10.1109/hpcc-smartcity-dss50907.2020.00195

Cited by 2 publications

(3 citation statements)

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“…The present work extends a previous contribution, [17], with the addition of new concepts and discussions, namely the formal proofs of correctness, the procedures for the switch setting, the evaluation of the energy consumption, and its application to the matrix transposition. The parts added to this version make the potential of the proposed method more evident.…”

Section: Introductionmentioning

confidence: 57%

“…To determine internal conflicts, the conflict window defined on the binary permutation matrix can be used, as described in [17]. The permutation matrix P for the Butterfly is obtained by concatenating the binary representation of each source S = s n−1 s n−2 .…”

Section: Background and Preliminariesmentioning

confidence: 99%

“…As described in [17], internal conflicts are detected checking the n − 1 possible conflict windows, each corresponding to a sub-matrix of P consisting of n consecutive columns.…”

Section: Background and Preliminariesmentioning

confidence: 99%

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Realizing Optimal All-to-All Personalized Communication Using Butterfly-Based Networks

Izzi

Massini

2023

IEEE Access

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The communication network is a key component in parallel and distributed systems, highperformance computing (HPC) systems and Data Centers, as information exchange has a key role in communication-intensive applications. The all-to-all personalized exchange is a relevant communication pattern and has been extensively studied for many network topologies. When considering a Multistage Interconnection Network (MIN) with log N stages, the realization of all-to-all communication is obtained through a sequence of admissible permutations forming a Latin square. If a particular Latin square is desired, double MINs consisting of 2 log N -1 stages are required. In this work, we consider the Butterfly-Butterfly network to realize the Latin square consisting of the identity permutation and its N − 1 rotations, RLS, and we show how to obtain the sequence of rotations forming such a Latin square, without storing it. We propose a method to realize the N permutations in pipeline fashion taking optimal O(N ) time, and we analyze the energy consumption according to the order of realization of the permutations, both on Butterfly-Butterfly network and on a single Butterfly used twice. We also show how to generate a Latin Square starting from any realizable permutation exploiting the switch configurations of the RLS.

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Section: Introductionmentioning

confidence: 57%

Section: Background and Preliminariesmentioning

confidence: 99%