# Coarse-Grained Parallelization of Distance-Bound Smoothing for the Molecular Conformation Problem

## Abstract

Determining the three-dimensional structure of proteins is crucial to efficient drug design and understanding biological processes. One successful method for computing the molecule’s shape relies on the inter-atomic distance bounds provided by the Nucleo-Magnetic Resonance (NMR) spectroscopy. The accuracy of computed structures as well as the time required to obtain them are greatly improved if the gaps between the upper and lower distance-bounds are reduced. These gaps are reduced most effectively by applying the tetrangle inequality, derived from the Cayley-Menger determinant, to all atom-quadruples. However, tetrangle-inequality bound-smoothing is an extremely computation intensive task, requiring *O*(*n* ^{4}) time for an *n*-atom molecule. To reduce the computation time, we propose a novel coarse-grained parallel algorithm intended for a Beowulf-type cluster of PCs. The algorithm employs *p n/6* processors and requires *O*(*n* ^{4}/*p*) time and *O*(*p* ^{2}) communications. The number of communications is at least an order of magnitude lower than in the earlier parallelizations. Our implementation utilized the processors with at least 59% efficiency (including the communication overhead) — an impressive figure for a nonembarrassingly parallel problem on a cluster of workstations.

## Keywords

Parallel Algorithm Communication Step Distance Geometry Molecular Conformation Problem Early Parallelizations## Preview

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