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.
Text
note.pdf - Author Accepted Manuscript Download (650kB) | Preview |
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 |