Journal of the European Mathematical Society· 2026Q1
Moser–Tardos Algorithm with small number of random bits
- 2citations
- Q1SCImago
- 2026year
Short summary
A variant of the Moser–Tardos Algorithm uses a constant, variable-independent number of random bits for problems with subexponential dependency graph growth, achieving O(n) deterministic runtime.
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Key points
- A parallel Moser–Tardos Algorithm variant uses a constant number of random bits for problems with subexponential dependency graph growth.
- Random bits are reused for variables far apart in the dependency graph.
- This leads to a deterministic algorithm with O(n) runtime for finding satisfying assignments.
- A Borel version of the Lovász Local Lemma is also presented.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study a variant of the parallel Moser–Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm is constant; in particular, it is independent of the number of variables. This is achieved by using the same random bits to resample variables which are far enough in the dependency graph. There are two corollaries. First, we obtain a deterministic algorithm for finding a satisfying assignment, which for any class of problems as in the previous paragraph runs in time O(n) , where n is the number of variables. Second, we present a Borel version of the Lovász Local Lemma.
The authors' abstract, as published at the source. Journal of the European Mathematical Society, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics