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Two words are called k-abelian equivalent, if they share the same multiplic-ities for all factors of length at most k. We present an optimal linear time algorithm for identifying all occurrences of factors in a text that are k-abelian equivalent to some pattern P. Moreover, an optimal algorithm for finding the largest k for which two words are k-abelian… (More)

We present new parallel sorting networks for 17 to 20 inputs. For 17, 19, and 20 inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on 17, 19, and 20 channels. Furthermore, we show that our sorting… (More)

We present new parallel sorting networks for 17 to 20 inputs. For 17, 19, and 20 inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore , we improve upon the known upper bounds for minimal depth sorting networks on 17, 19, and 20 channels. The networks were obtained using a… (More)

The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set Problem (FASP) to make the graph acyclic before a layering is determined. Here we present the Generalized Layering Problem… (More)

This paper studies new properties of the front and back ends of a sorting network, and illustrates the utility of these in the search for new bounds on optimal sorting networks. Search focuses first on the " outsides " of the network and then on the inner part. All previous works focus only on properties of the front end of networks and on how to apply… (More)

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