A Faster Algorithm for Finding Tarski Fixed Points



Fearnley, John, Palvolgyi, Domotor and Savani, Rahul ORCID: 0000-0003-1262-7831
(2022) A Faster Algorithm for Finding Tarski Fixed Points. ACM TRANSACTIONS ON ALGORITHMS, 18 (3). 29:1-29:1.

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Abstract

Dang et al. have given an algorithm that can find a Tarski fixed point in a k-dimensional lattice of width n using O(log k n) queries [2]. Multiple authors have conjectured that this algorithm is optimal [2, 7], and indeed this has been proven for two-dimensional instances [7]. We show that these conjectures are false in dimension three or higher by giving an O(log2 n) query algorithm for the three-dimensional Tarski problem. We also give a new decomposition theorem for k-dimensional Tarski problems which, in combination with our new algorithm for three dimensions, gives an O(log2 [k/3]permil; n) query algorithm for the k-dimensional problem.

Item Type: Article
Uncontrolled Keywords: Query complexity, Tarski fixed points, total function problem
Depositing User: Symplectic Admin
Date Deposited: 18 Jan 2021 09:40
Last Modified: 15 Mar 2024 01:26
DOI: 10.1145/3524044
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3113755