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Jens Gerlach

Publications and source records attributed to Jens Gerlach.

2 recordsLinked to original sources
arXiv2013

Sorting in Lattices

In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are related to those of its sorted counterpart. As this formula relies only on the minimum and maximum functions we use it to define the notion of sorting for lattices. A major difference of sorting in lattices is that it does not guarantee that sequence elements are only rearranged. However, we can show that other fundamental properties that are associated with sorting are preserved.

cs.DM↗
arXiv2013

Recursive Sorting in Lattices

The direct application of the definition of sorting in lattices is impractical because it leads to an algorithm with exponential complexity. In this paper we present for distributive lattices a recursive formulation to compute the sort of a sequence. This alternative formulation is inspired by the identity that underlies Pascal's triangle. It provides quadratic complexity and is in fact a generalization of insertion sort for lattices.

cs.DM↗