We consider a system of <i>N</i> parallel queues with unit exponential service rates and a single dispatcher where tasks arrive as a Poisson process of rate λ(<i>N</i>). When a task arrives, the dispatcher assigns it to a server with the shortest queue among <i>d</i>(<i>N</i>) ≤ <i>N</i> randomly selected servers. This load balancing policy is… (More)
The k-section width and the Max-Cut for the configuration model are shown to exhibit phase transitions according to the values of certain parameters of the asymptotic degree distribution. These transitions mirror those observed on Erd˝ os-Rényi random graphs, established by Luczak and McDiarmid (2001), and Coppersmith et al. (2004), respectively.
Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In this paper, rather than asking this question from an algorithmic perspective, we analyze the combinatorial structure… (More)
We fix three natural numbers k, n, N , such that n + k + 1 = N , and introduce the notion of two dual arrangements of hyperplanes. One of the arrangements is an arrangement of N hyperplanes in a k-dimensional affine space, the other is an arrangement of N hyperplanes in an n-dimensional affine space. We assign weights α 1 ,. .. , α N to the hyperplanes of… (More)