Abstract
First we give an optimal EREW PRAM algorithm that finds an unknown discrete monotone function ƒ, with domain and range of size n, in O( log n) time using O( n) independent threshold queries of kind “ƒ(x) ⩾ y?”. Here “independent” means that simultaneous queries always refer to mutually disjoint values x and y. This is used for solving, within the same resources, a certain segmentation problem for words over semigroups. The classical problem of partitioning a digital curve into a minimum number of digital line segments, which is of interest in digital image processsing, turns out to be a special case of this, and can therefore be solved in O( log n) time using O( n) work on an EREW PRAM. This strengthens and generalizes all known algorithmic results about digital curve segmentation. As a further prerequisite we use the Dorst-Smeulders parametrization of digital line segments.
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