Equitable Coloring Extends Chernoff-Hoeffding Bounds

Randomized Distributed Edge Coloring via an Extension of the Chernoff-Hoeffding Bounds

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 ∆ with at most 1.6∆+O(log n) co...

Lecture 03 : Chernoff Bounds and Intro to Spectral Graph Theory 3 1 . 1 Hoeffding ’ s Inequality

A note on the distribution of the number of prime factors of the integers

The Chernoff-Hoeffding bounds are fundamental probabilistic tools. An elementary approach is presented to obtain a Chernoff-type upper-tail bound for the number of prime factors of a random integer in {1, 2, . . . , n}. The method illustrates tail bounds in negatively-correlated settings.

Chernoff-Hoeffding Bounds for Markov Chains: Generalized and Simplified

We prove the first Chernoff-Hoeffding bounds for general (nonreversible) finite-state Markov chains based on the standard L1 (variation distance) mixing-time of the chain. Specifically, consider an ergodic Markov chain M and a weight functionf : [n] → [0, 1] on the state space [n] of M with mean μ , Ev←π[f(v)], where π is the stationary distribution of M . A t-step random walk (v1, . . . , vt) ...

Hypothesis testing for Gaussian states on bosonic lattices

The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein’s lemma in the case when both hypotheses are gauge-invariant Gaussian states with translation-invariant quasi-free parts.