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- W3173624684 abstract "We present a randomized algorithm which takes as input an undirected graph $G$ on $n$ vertices with maximum degree $Delta$, and a number of colors $k geq (8/3 + o_{Delta}(1))Delta$, and returns -- in expected time $tilde{O}(nDelta^{2}log{k})$ -- a proper $k$-coloring of $G$ distributed perfectly uniformly on the set of all proper $k$-colorings of $G$. Notably, our sampler breaks the barrier at $k = 3Delta$ encountered in recent work of Bhandari and Chakraborty [STOC 2020]. We also sketch how to modify our methods to relax the restriction on $k$ to $k geq (8/3 - epsilon_0)Delta$ for an absolute constant $epsilon_0 > 0$. As in the work of Bhandari and Chakraborty, and the pioneering work of Huber [STOC 1998], our sampler is based on Coupling from the Past [ProppW Haggstrom&Nelander, Scand. J. Statist., 1999]. Our innovations include a novel bounding chain routine inspired by Jerrum's analysis of the Glauber dynamics [Random Struct. Algorithms, 1995], as well as a preconditioning routine for bounding chains which uses the algorithmic Lovasz Local Lemma [Moser&Tardos, J.ACM, 2010]." @default.
- W3173624684 created "2021-07-05" @default.
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- W3173624684 date "2021-06-21" @default.
- W3173624684 modified "2023-09-23" @default.
- W3173624684 title "Perfectly Sampling kgeq (8/3 +o(1))Delta-Colorings in Graphs" @default.
- W3173624684 hasPublicationYear "2021" @default.
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