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Motivated by the problem of link scheduling in wireless sensor networks where different sensors have different transmission and interference ranges and may be mobile, we study the problem of "distance edge coloring" of graphs, which is a generalization of proper edge coloring. Let G be a graph modeling a sensor network. An -distance edge coloring of G is a coloring of the edges of G such that any two edges within distance of each other are assigned different colors. The parameter is chosen, so that the links corresponding to two edges that are assigned the same color do not interfere. We investigate the -distance edge coloring problem on several families of graphs that can be used as topologies in sensor deployment. We focus on determining the minimum number of colors needed and optimal coloring algorithms.

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This paper addresses dynamic bandwidth allocation for virtual network (VN) resources to respond to increasing or decreasing applications requirements in cloud environments. A distributed and local-view framework, composed of a controller and three algorithms running in substrate nodes, is proposed to deal with all types of bandwidth demand fluctuations in embedded virtual networks. The framework is based on the Self-Stabilization concept to drive the system back to a "stable state" when new bandwidth demands drift the system away into an "unstable state". Performance evaluation results demonstrate the effectiveness of our proposal in handling bandwidth demand fluctuations in convergence speed and cost. Index Terms-Virtual network embedding, dynamic bandwidth allocation, elasticity, self stabilization, local view, cloud, distributed and parallel algorithms; We opt for a self-stabilizing approach to manage bandwidth demand fluctuation. We will first introduce the Selfstabilization concept and motivate this choice, then, we will describe our solution.