
Ultrafast Distributed Coloring of High Degree Graphs
We give a new randomized distributed algorithm for the Δ+1list coloring...
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Seeing Far vs. Seeing Wide: Volume Complexity of Local Graph Problems
Consider a graph problem that is locally checkable but not locally solva...
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Generalizing the Sharp Threshold Phenomenon for the Distributed Complexity of the Lovász Local Lemma
Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted ...
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An Optimal Distributed (Δ+1)Coloring Algorithm?
Vertex coloring is one of the classic symmetry breaking problems studied...
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Improved LCAs for constructing spanners
In this paper we study the problem of constructing spanners in a local m...
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Local Computation Algorithms for Spanners
A graph spanner is a fundamental graph structure that faithfully preserv...
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Reproducibility and PseudoDeterminism in LogSpace
A curious property of randomized logspace search algorithms is that the...
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The randomized local computation complexity of the Lovász local lemma
The Local Computation Algorithm (LCA) model is a popular model in the field of sublineartime algorithms that measures the complexity of an algorithm by the number of probes the algorithm makes in the neighborhood of one node to determine that node's output. In this paper we show that the randomized LCA complexity of the Lovász Local Lemma (LLL) on constant degree graphs is Θ(log n). The lower bound follows by proving an Ω(log n) lower bound for the Sinkless Orientation problem introduced in [Brandt et al. STOC 2016]. This answers a question of [Rosenbaum, Suomela PODC 2020]. Additionally, we show that every randomized LCA algorithm for a locally checkable problem with a probe complexity of o(√(logn)) can be turned into a deterministic LCA algorithm with a probe complexity of O(log^* n). This improves exponentially upon the currently best known speedup result from o(loglog n) to O(log^* n) implied by the result of [Chang, Pettie FOCS 2017] in the LOCAL model. Finally, we show that for every fixed constant c ≥ 2, the deterministic VOLUME complexity of ccoloring a bounded degree tree is Θ(n), where the VOLUME model is a close relative of the LCA model that was recently introduced by [Rosenbaum, Suomela PODC 2020].
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