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The problem of grooming is central in studies of optical networks. In graph-theoretic terms, this can be viewed as assigning colors to the lightpaths so that at most g of them (g being the grooming factor) can share one edge. The cost of a coloring is the number of optical switches (ADMs); each lightpath uses two ADM's, one at each endpoint, and in case g… (More)

The placement of regenerators in optical networks has become an active area of research during the last few years. Given a set of lightpaths in a network <i>G</i> and a positive integer <i>d</i>, regenerators must be placed in such a way that in any lightpath there are no more than <i>d</i> hops without meeting a regenerator. The cost function we consider… (More)

We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J 1 ,. .. , J n }. Each job, J j , is associated with an interval [s j , c j ] along which it should be processed. Also given is the parallelism parameter g ≥ 1, which is the maximal number of jobs that… (More)

—We consider the following fundamental scheduling problem in which the input consists of n jobs to be scheduled on a set of identical machines of bounded capacity g (which is the maximal number of jobs that can be processed simultaneously by a single machine). Each job is associated with a start time and a completion time; it is supposed to be processed… (More)

Given a tree and a set P of non-trivial simple paths on it, Vpt(P) is the VPT graph (i.e. the vertex intersection graph) of the paths P of the tree T , and Ept(P) is the EPT graph (i.e. the edge intersection graph) of P. These graphs have been extensively studied in the literature. Given two (edge) intersecting paths in a graph, their split vertices is the… (More)