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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)

- D Mukherjee, A Varchenko
- 2006

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)

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