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- W4221151522 abstract "We study the query complexity of finding a Tarski fixed point over the k-dimensional grid {1,...,n}k. Improving on the previous best upper bound of O(log⌈2k/3⌉n)[7], we give a new algorithm with query complexity O(log⌈(k+1)/2⌉n). This is based on a novel decomposition theorem about a weaker variant of the Tarski fixed point problem, where the input consists of a monotone function f:[n]k→[n]k and a monotone sign function b:[n]k→ {-1,0,1} and the goal is to find a point x ∈ [n]k that satisfies either f(x) ≼ x and b(x) ≤ 0 or f(x) ≽ x and b(x) ≥ 0." @default.
- W4221151522 created "2022-04-03" @default.
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- W4221151522 date "2022-07-12" @default.
- W4221151522 modified "2023-10-15" @default.
- W4221151522 title "Improved Upper Bounds for Finding Tarski Fixed Points" @default.
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- W4221151522 doi "https://doi.org/10.1145/3490486.3538297" @default.
- W4221151522 hasPublicationYear "2022" @default.
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