[2411.18028] Improved Parallel Derandomization via Finite Automata with Applications
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Computer Science > Data Structures and Algorithms

arXiv:2411.18028 (cs)
[Submitted on 27 Nov 2024]

Title:Improved Parallel Derandomization via Finite Automata with Applications

Authors:Jeff Giliberti, David G. Harris
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Abstract:One main genre of algorithmic derandomization comes from the construction of probability distributions with small support that fool a randomized algorithm. This is especially well-suited to parallelization, i.e. NC algorithms. A significant abstraction of these methods can be formulated in terms of fooling polynomial-space statistical tests computed via finite automata (Sivakumar 2002); this encompasses $k$-wise independence, sums of random variables, and many other properties.
We describe new parallel algorithms to fool general finite-state automata with significantly reduced processor complexity. The analysis is also simplified because we can cleanly separate the problem-specific optimizations from the general lattice discrepancy problems at the core of the automaton-fooling construction. We illustrate with improved applications to the Gale-Berlekamp Switching Game and to approximate MAX-CUT via SDP rounding.
Subjects: Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2411.18028 [cs.DS]
  (or arXiv:2411.18028v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2411.18028

Submission history

From: Jeff Giliberti [view email]
[v1] Wed, 27 Nov 2024 03:50:15 UTC (28 KB)
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