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- W2616078511 abstract "Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded degree graphs) that has an $o(log n)$-round randomized algorithm can be solved in $T_{LLL}(n)$ rounds, which is the randomized complexity of solving (a relaxed variant of) the Lovasz Local Lemma (LLL) on bounded degree $n$-node graphs. Currently, the best known upper bound on $T_{LLL}(n)$ is $O(log n)$, by Chung, Pettie, and Su [PODC'14], while the best known lower bound is $Omega(loglog n)$, by Brandt et al. [STOC'16]. Chang and Pettie conjectured that there should be an $O(loglog n)$-round algorithm. Making the first step of progress towards this conjecture, and providing a significant improvement on the algorithm of Chung et al. [PODC'14], we prove that $T_{LLL}(n)= 2^{O(sqrt{loglog n})}$. Thus, any $o(log n)$-round randomized distributed algorithm for any LCL problem on bounded degree graphs can be automatically sped up to run in $2^{O(sqrt{loglog n})}$ rounds. Using this improvement and a number of other ideas, we also improve the complexity of a number of graph coloring problems (in arbitrary degree graphs) from the $O(log n)$-round results of Chung, Pettie and Su [PODC'14] to $2^{O(sqrt{loglog n})}$. These problems include defective coloring, frugal coloring, and list vertex-coloring." @default.
- W2616078511 created "2017-05-26" @default.
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- W2616078511 date "2017-05-13" @default.
- W2616078511 modified "2023-09-27" @default.
- W2616078511 title "Sublogarithmic Distributed Algorithms for Lov'asz Local lemma, and the Complexity Hierarchy" @default.
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