Pick-and choose heuristics for partial set covering
Discrete Applied Mathematics
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Computing the arrangement of circles on a sphere, with applications in structural biology
Computational Geometry: Theory and Applications
Efficient algorithms to explore conformation spaces of flexible protein loops
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
Computing the volume of a union of balls: A certified algorithm
ACM Transactions on Mathematical Software (TOMS)
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To address challenging flexible docking problems, a number of docking algorithms pregenerate large collections of candidate conformers. To remove the redundancy from such ensembles, a central problem in this context is to report a selection of conformers maximizing some geometric diversity criterion. We make three contributions to this problem. First, we resort to geometric optimization so as to report selections maximizing the molecular volume or molecular surface area (MSA) of the selection. Greedy strategies are developed, together with approximation bounds. Second, to assess the efficacy of our algorithms, we investigate two conformer ensembles corresponding to a flexible loop of four protein complexes. By focusing on the MSA of the selection, we show that our strategy matches the MSA of standard selection methods, but resorting to a number of conformers between one and two orders of magnitude smaller. This observation is qualitatively explained using the Betti numbers of the union of balls of the selection. Finally, we replace the conformer selection problem in the context of multiple-copy flexible docking. On the aforementioned systems, we show that using the loops selected by our strategy can improve the result of the docking process.