Deterministic APSP, Orthogonal Vectors, and More: Quickly Derandomizing Razborov-Smolensky
Name
detapsp_soda.pdf
Description
Accepted version
Size
243.91 KB
Format
Adobe PDF
Checksum (MD5)
e2401696791d70437ef43ad2cfee5441
Author(s)
Chan, Timothy M
Williams, R Ryan
Date Issued
2021
Journal
ACM Transactions on Algorithms
Publisher
Association for Computing Machinery (ACM)
Citation
Chan, Timothy M and Williams, R Ryan. 2021. "Deterministic APSP, Orthogonal Vectors, and More: Quickly Derandomizing Razborov-Smolensky." ACM Transactions on Algorithms, 17 (1).
Version
Author's final manuscript
Abstract
© 2020 ACM. We show how to solve all-pairs shortest paths on n nodes in deterministic n3>/2>ω (s log n) time, and how to count the pairs of orthogonal vectors among n 0-1 vectors in d = clog n dimensions in deterministic n2-1/O(log c) time. These running times essentially match the best known randomized algorithms of Williams [46] and Abboud, Williams, and Yu [8], respectively, and the ability to count was open even for randomized algorithms. By reductions, these two results yield faster deterministic algorithms for many other problems. Our techniques can also be used to deterministically count k-satisfiability (k-SAT) assignments on n variable formulas in 2n-n/O(k) time, roughly matching the best known running times for detecting satisfiability and resolving an open problem of Santhanam [24]. A key to our constructions is an efficient way to deterministically simulate certain probabilistic polynomials critical to the algorithms of prior work, carefully applying small-biased sets and modulus-amplifying polynomials.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/3402926
