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In this paper the process of data transmission in optical communication networks is modeled as a shop-type scheduling problem, where channels (wavelengths) are treated as machines. We formulate an Open Block problem with the minimum makespan objective (an problem) in which a relation of a new type between the operations of each job is introduced: any two operations of a job...
This paper deals with vector covering problems in d-dimensional space. The input to a vector covering problem consists of a set X of d-dimensional vectors in [0, 1]d. The goal is to partition X into a maximum number of parts, subject to the constraint that in every part the sum of all vectors is at least one in every coordinate. This problem is known to be NP-complete, and we are mainly interested...
In this paper, we demonstrate the existence of a polynomial time approximation scheme for makespan minimization in the open shop scheduling problem with an arbitrary fixed number m of machines. For the variant of the problem where the number of machines is part of the input, it is known that the existence of an approximation scheme would imply P=NP. Hence, our result draws a precise separating line...
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