Randomized Distributed Edge Coloring via an Extension of the Chernoff--Hoeffding Bounds
TLDR
Fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point model of computation and new techniques for proving upper bounds on the tail probabilities of certain random variables which are not stochastically independent are introduced.Abstract:
Certain types of routing, scheduling, and resource-allocation problems in a distributed setting can be modeled as edge-coloring problems We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point model of computation Our algorithms compute an edge coloring of a graph $G$ with $n$ nodes and maximum degree $\Delta$ with at most $16 \Delta + O(\log^{1+ \delta} n)$ colors with high probability (arbitrarily close to 1) for any fixed $\delta > 0$; they run in polylogarithmic time The upper bound on the number of colors improves upon the $(2 \Delta - 1)$-coloring achievable by a simple reduction to vertex coloring
To analyze the performance of our algorithms, we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables The Chernoff--Hoeffding bounds are fundamental tools that are used very frequently in estimating tail probabilities However, they assume stochastic independence among certain random variables, which may not always hold Our results extend the Chernoff--Hoeffding bounds to certain types of random variables which are not stochastically independent We believe that these results are of independent interest and merit further studyread more
Citations
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Locally-Iterative Distributed (Δ+ 1): -Coloring below Szegedy-Vishwanathan Barrier, and Applications to Self-Stabilization and to Restricted-Bandwidth Models
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The Johansson‐Molloy theorem for DP‐coloring
TL;DR: A streamlined version of Molloy's new proof of the bound for triangle-free graphs, avoiding the technicalities of the entropy compression method and only using the usual "lopsided" Lov\'asz Local Lemma (albeit in a somewhat unusual setting).
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Streaming algorithms for estimating the matching size in planar graphs and beyond
Hossein Esfandiari,MohammadTaghi Hajiaghayi,Vahid Liaghat,Morteza Monemizadeh,Krzysztof Onak +4 more
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Approximation Algorithms for Stochastic and Risk-Averse Optimization
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The Moser-Tardos Framework with Partial Resampling
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