General asymptotic rank speedup theorems are established via Strassen calculus, proving the asymptotic rank of cw_2 is below 3.931 and yielding an upper bound below d^{2ω/3} for any d×d×d tensor.
Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pages=
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New parallel algorithms achieve Õ(m) work and o(√n) depth for reachability and shortest paths on directed graphs whenever m ≥ n^{1+o(1)}, improving on the prior Ω(√n) depth barrier.
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Asymptotic Rank Speedup Theorems, Revisited
General asymptotic rank speedup theorems are established via Strassen calculus, proving the asymptotic rank of cw_2 is below 3.931 and yielding an upper bound below d^{2ω/3} for any d×d×d tensor.
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Parallel Reachability and Shortest Paths on Non-sparse Digraphs: Near-linear Work and Sub-square-root Depth
New parallel algorithms achieve Õ(m) work and o(√n) depth for reachability and shortest paths on directed graphs whenever m ≥ n^{1+o(1)}, improving on the prior Ω(√n) depth barrier.