Karl-Heinz Zimmermann

Efficient DNA sticker algorithms for NP-complete graph problems

Adlemans successful solution of a seven-vertex instance of the NP-complete Hamiltonian directed path problem by a DNA algorithm initiated the field of biomolecular computing. We provide DNA algorithms based on the sticker model to compute all k-cliques, independent k-sets, Hamiltonian paths, and Steiner trees with respect to a given edge or vertex set. The algorithms determine not merely the existence of a solution but yield all solutions (if any). For an undirected graph with n vertices and m edges, the running time of the algorithms is linear in n+m. For this, the sticker algorithms make use of small combinatorial input libraries instead of commonly used large libraries. The described algorithms are entirely theoretical in nature. They may become very useful in practice, when further advances in biotechnology lead to an efficient implementation of the sticker model.

On generalizations of repeated-root cyclic codes

We first consider repeated-root cyclic codes, i.e., cyclic codes whose block length is divisible by the characteristic of the underlying field. It is well known that the formula for the minimum distance of repeated-root cyclic codes is similar to that for generalized concatenated codes. We show that indecomposable repeated-root cyclic codes are product codes and that the minimum weight of each repeated-root cyclic code is attained by one of its subcodes being equivalent to a product code. We then generalize the coding theoretical results on repeated-root cyclic codes to a larger class of left ideals in group algebra F/sub p/m/spl Gscr/ defined on non-Abelian groups, namely, groups /spl Gscr/ containing a normal cyclic Sylow p-subgroup. We show that a class of these codes compares reasonably to (shortened) generalized Reed-Muller codes over the primes and finally indicate by the special linear group SL/sub 2/(F/sub p/) how a further generalization may in principle be settled.

Linear mappings ofn-dimensional uniform recurrences ontok-dimensional systolic arrays

We propose two methods for the synthesis of systolic arrays from uniform recurrence equations. First, we discuss a synthesis method for mappingn-dimensional uniform recurrence equations ontok-dimensional systolic arrays with a two-dimensional system clock. In this method we are led by the idea that all space-time conflicts caused by a scalar valued causal timing function and an allocation function can be rule out by a second scalar valued timing function. Stacking both timing functions yields a two-dimensional clock. Second, we develop a method to synthesizek-dimensional arrays with a scalar valued clock from a large subclass ofn-dimensional uniform recurrence equations containing important algorithms from signal and image processing. This method is based on a decomposition of the domain of the uniform recurrence equations into subdomains according to a given procesor allocation which allows the construction of a timing function for the whole domain from timing functions for the subdomains. In this way, the problem of finding optimal timing functions is reduced to finding optimal functions for the subdomains which are usually easier to establish. This synthesis method exhibits simplicity but its drawback lies in its limited applicability.

Combinatorial S >n -Modules as Codes

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Parallel bioinspired algorithms for NP complete graph problems

\mathbb{Z}S_n

D-Bees: A novel method inspired by bee colony optimization for solving word sense disambiguation

-modules related to the kernels ofincidence maps between types in the poset defined by the natural productorder on the set of n-tuples with entries from {1,

Two new nonlinear binary codes

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