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Graph partitioning divides a graph into several pieces by cutting edges. The graph partitioning problem is to divide so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges separating these pieces is minimised. Important examples of the problem arise in partitioning graphs known as meshes for the(More)
Graph partitioning divides a graph into several pieces by cutting edges. The graph partitioning problem is to divide so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges separating these pieces is minimised. Important examples of the problem arise in partitioning graphs known as meshes for the(More)
1. We have studied the characteristics of the abnormal properties of damaged myelinated fibers (conduction velocity > 2.0 m/ s) after peripheral nerve injury in a novel in vitro model of the rat sciatic nerve/dorsal root ganglion/dorsal root (L4-5) preparation removed from control naíve or sham-operated rats and animals that had received sciatic neurectomy(More)
For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preempt-ive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2 − 1/m is tight. If the makespan of the(More)
In this paper we discuss an efficiency saving for multilevel force directed placement algorithms. Typically such algorithms use a Barnes Hut octree (or sometimes a grid) in order to approximate global repulsive forces. Here we instead exploit the graph coarsening structure, already in place to facilitate the multilevel scheme, in order to provide a(More)
This paper presents two multilevel refinement algorithms for the capacitated clustering problem. Multilevel refinement is a collaborative technique capable of significantly aiding the solution process for optimisation problems. The central methodologies of the technique are filtering solutions from the search space and reducing the level of problem detail(More)