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We consider the problem of rounding the entries of a matrix without distorting the row, column, and grand totals. This problem arises in controlling statistical disclosure, in data analysis, and elsewhere. There are algorithms in the literature which produce roundings that are “tight” in the...
We propose here a systematic formal study of the splicing operation introduced by Head as a model of recombinant behavior of DNA. We consider both simple and iterated splicing, with respect to a finite or an infinite set of splicing rules, in the latter case the whole set of rules constituting a...
For a fixed oriented tree T , we consider the complexity of deciding whether or not a given digraph G is homomorphic to T . It was shown by Gutjahr, Woeginger and Welzl that there exist trees T for which this homomorphism problem is NP-complete. However, it seems difficult to decide just which...
Consider a set of circles of the same length and r irregular polygons with vertices on a circle of this length. Each of the polygons has to be arranged on a given subset of all circles and the positions of the polygon on the different circles are depending on each other. How should the polygons...
We consider a parallel machine scheduling problem in which the processing time of a job is a simple linear function of its starting time. The objective is to minimize total completion times. We show that the problem is NP-hard in the strong sense even with a fixed number of machines. When the...
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