2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) 2016
DOI: 10.1109/focs.2016.73
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Abstract: Locally finding a solution to symmetry-breaking tasks such as vertex-coloring, edge-coloring, maximal matching, maximal independent set, etc., is a long-standing challenge in distributed network computing. More recently, it has also become a challenge in the framework of centralized local computation. We introduce conflict coloring as a general symmetry-breaking task that includes all the aforementioned tasks as specific instantiations -conflict coloring includes all locally checkable labeling tasks from [Naor… Show more

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Cited by 99 publications
(159 citation statements)
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References 43 publications
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“…Panconesi and Rizzi provide an O(∆ + log * n) algorithm for (2∆ − 1)-edge-coloring. This complexity was recently improved by Barenboim [Bar15] to O(∆ 3/4 log ∆ + log * n) and subsequently to O(∆ 1/2 log 5/2 ∆ + log * n) by Fraigniaud, Heinrich, and Kosowski [FHK16]. Both these results work indeed for the harder problem of (∆ + 1)-vertex coloring.…”
Section: Degree Splitting and Edge Orientationssupporting
confidence: 53%
“…Panconesi and Rizzi provide an O(∆ + log * n) algorithm for (2∆ − 1)-edge-coloring. This complexity was recently improved by Barenboim [Bar15] to O(∆ 3/4 log ∆ + log * n) and subsequently to O(∆ 1/2 log 5/2 ∆ + log * n) by Fraigniaud, Heinrich, and Kosowski [FHK16]. Both these results work indeed for the harder problem of (∆ + 1)-vertex coloring.…”
Section: Degree Splitting and Edge Orientationssupporting
confidence: 53%
“…Note that all t j are elements of R 3 ≥0 as they are weighted averages of elements in R 3 ≥0 , by the characterization of the t j given above. [FHK16]. Then, we iterate through the color classes and every node of a color class fixes, one by one but in a single communication round, all of its variables that are not fixed yet.…”
Section: Proof Of the Variable Fixing Lemma (Lemma 32)mentioning
confidence: 99%
“…Then, we iterate through the color classes and fix all the random variables of the nodes in the current color class. Using the algorithm by Fraigniaud, Heinrich and Kosowski, the coloring can be found in O(d) + log * n time [FHK16].…”
Section: Introductionmentioning
confidence: 99%
“…Together with the best known randomized algorithms (which use the shattering technique), the algorithm of [FGK17] also implied that the (2∆ − 1)-edge coloring problem has a randomized complexity of poly log log n. The current best time complexities for computing an (2∆ − 1)-edge coloring in general graphs areÕ(log 2 ∆ log n) for the deterministic andÕ(log 3 log n) for the randomized setting [Har18]. For small values of ∆, the best known complexity is O( √ ∆ log ∆ log * ∆+log * n) [FHK16,BEG18], as for computing a (∆+1)-vertex coloring. As one of our contributions, we improve this last result to 2 O( √ log ∆) + O(log * n).…”
Section: Randomized Distributedmentioning
confidence: 99%