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In this paper we consider the problem of (<i>k</i>, <i>υ</i>)-balanced graph partitioning - dividing the vertices of a graph into <i>k</i> almost equal size components (each of size less than <i>υ</i> • <i>n</i><over><i>k</i>) so that the capacity of edges between different components is minimized. This problem is a natural… (More)

In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within alogarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai… (More)

We consider the problem of simultaneous source location: selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied simultaneously, with the goal of minimizing the number of locations chosen. For general directed and undirected graphs we give an <i>O</i>(log <i>D</i>)-approximation algorithm, where <i>D</i> is… (More)

In this paper, we present a polynomial time approximation algorithm for constructing an overlay multicast network for streaming live media events over the Internet. The class of overlay networks constructed by our algorithm include networks used by Akamai Technologies to deliver live media events to a global audience with high fidelity. In particular, we… (More)

A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations , which are qualitatively similar to oscillations generating by Rose–Hindmarsh model. The synchronization in small ensembles of the maps is investigated. It is… (More)

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