A Faster Algorithm for Finding Tarski Fixed Points

被引：1
|
作者：
Fearnley, John [1 ]
Palvolgyi, Domotor [2 ]
Savani, Rahul [1 ]
机构：
[1] Univ Liverpool, Dept Comp Sci, Ashton Bldg Ashton St, Liverpool L69 3BX, Merseyside, England
[2] Eotvos Lorand Univ, Inst Math, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary
来源：
ACM TRANSACTIONS ON ALGORITHMS | 2022年 / 18卷 / 03期
关键词：
Query complexity; Tarski fixed points; total function problem; EQUILIBRIUM; COMPLEXITY; GAMES;
D O I：
10.1145/3524044
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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(log(2) 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(log(2) left perpendicular (k/3) right perpendicular n) query algorithm for the k-dimensional problem.
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页数：23
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