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Starting from a batch scheduling problem, we consider a weighted subcoloring in a graph G; each node v has a weight w(v); each color class S is a subset of nodes which generates a collection of node disjoint cliques. The weight w(S) is defined as max{w(K)=∑v∈Kw(v)|K∈S}. In the scheduling problem, the completion time is given by ∑i=1kw(Si) where S=(S1,…,Sk) is a partition of the node set of graph G...
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