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We consider the problem of randomly rounding a fractional solution x in an integer polytope P ⊆ [0,1]n to a vertex X of P, so that E[X] = x. Our goal is to achieve concentration properties for linear and submodular functions of the rounded solution. Such dependent rounding techniques, with concentration bounds for linear functions, have been developed in the past for two poly topes: the assignment...
The hardcore model is a model of lattice gas systems which has received much attention in statistical physics, probability theory and theoretical computer science. It is the probability distribution over independent sets I of a graph weighted proportionally to λ|I| with fugacity parameter λ. We prove that at the uniqueness threshold of the hardcore model on the d-regular tree, approximating the partition...
Many relationships naturally come in a bipartite setting: authors that write articles, proteins that interact with genes, or customers that buy, rent or rate products. Often we are interested in the clustering behavior of one side of the graph, i.e., in finding groups of similar articles or products. To find these clusters, a one-mode projection is classically applied, which results in a normal graph...
We develop a computational framework to study the impact of burst assembly algorithms on the byte loss rate (ByLR) of an OBS network under bursty (ON-OFF) IP traffic input. First we propose a computational method to analyze the characteristics of assembled bursts in terms of burst length and/or burst assembly time distribution under timer-based, burst-threshold-based, and dual-threshold-based burst...
Distortion exponent has been proposed as performance measure to characterize how fast the average distortion decays to zero when the SNR increases to infinity. The distortion exponent for multiple description coding (MDC) has only been investigated for two descriptions and symmetric SNR. In this paper, we consider the case of any number of descriptions and asymmetric SNR. We derive an achievable distortion...
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