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In this paper, we revisit Bruck's All-to-All implementation and demonstrate the benefits of topology optimization in which both communication pattern and reconfiguration strategy are co-designed. We present ReTri, a bidirectional All-to-All schedule for ORNs based on the Trivance algorithm. ReTri uses balanced ternary block propagation to complete All-to-All in $\lceil \log_3 n\rceil$ phases. The reconfiguration strategy induced by ReTri's pairwise bidirectional exchanges allows reconfiguration delays to be amortized across multiple phases. Preliminary simulations show that ReTri improves completion time by up to $10\times$ over Pairwise All-to-All, even for millisecond-scale reconfiguration delays, and improves reconfigurable Bruck by up to $2.1\times$.
From: Anton Juerss [view email]
[v1]
Tue, 26 May 2026 12:24:04 UTC (1,007 KB)
[v2]
Thu, 9 Jul 2026 20:49:11 UTC (975 KB)
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