The smallest enclosing ball of balls

Fischer, Kaspar; Gärtner, Bernd

doi:10.1145/777833.777836

Cited by 6 publications

(5 citation statements)

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“…The disc must be created to fulfill Definition 4.1: it must cut the tunnel at one place only and it must cut it completely. The function recursively builds a set of spheres C ⊂ T, which contain P or intersect both ρ and some sphere in C. Having the C constructed, the algorithm projects spheres from C to ρ and computes the circle encapsulating all projected spheres using the algorithm [7]. The computed circle determines the center and the radius of the computed disc, the normal of the disc is the same as the normal of ρ.…”

Section: Helpermentioning

confidence: 99%

CaverDock: A Novel Method for the Fast Analysis of Ligand Transport

Filipovič

Vávra

Plhák

et al. 2020

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Here we present a novel method for the analysis of transport processes in proteins and its implementation called CaverDock. Our method is based on a modified molecular docking algorithm. It iteratively places the ligand along the access tunnel in such a way that the ligand movement is contiguous and the energy is minimized. The result of CaverDock calculation is a ligand trajectory and an energy profile of transport process. CaverDock uses the modified docking program Autodock Vina for molecular docking and implements a parallel heuristic algorithm for searching the space of possible trajectories. Our method lies in between the geometrical approaches and molecular dynamics simulations. Contrary to the geometrical methods, it provides an evaluation of chemical forces. However, it is far less computationally demanding and easier to set up compared to molecular dynamics simulations. CaverDock will find a broad use in the fields of computational enzymology, drug design and protein engineering. The software is available free of charge to the academic users at https://loschmidt.chemi.muni.cz/caverdock/.

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Section: Helpermentioning

confidence: 99%

CaverDock: A Novel Method for the Fast Analysis of Ligand Transport

Filipovič

Vávra

Plhák

et al. 2020

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…Once the radius is within some bound ρ, it can be shown that every agent's state is within 2ρ of the consensus value. We remark that even in the p − norm case determination of a minimum norm ball in a distributed manner is a difficult problem (see [45]). Here, we provide an algorithm which distributedly finds an approximation of minimal ball at each agent.…”

Section: Norm Based Finite-time Terminationmentioning

confidence: 99%

Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension

Melbourne¹,

Saraswat²,

Khatana³

et al. 2020

Preprint

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We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited for use in the absence of a central authority. A central application is to consensus algorithms in higher dimension. These pursuits motivate a new peer to peer convex hull algorithm which we demonstrate to be an instantiation of the described theory. To address the diversity of convex sets and the potential computation and communication costs of knowing such sets in high dimension, a lightweight norm based stopping criteria is developed. More explicitly, we give a distributed algorithm that terminates in finite time when applied to consensus problems in higher dimensions and guarantees the convergence of the consensus algorithm in norm, within any given tolerance. Applications to consensus least squared estimation and distributed function determination are developed. The practical utility of the algorithm is illustrated through MATLAB simulations.

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“…We investigate the problem of removing degeneracies in a class of optimization problems known as LP-type problems (or "generalized linear programming problems"). This axiomatic framework, invented by Sharir and Welzl in 1992 [19], has become a well-established tool in the field of geometric optimization; see [17,1,2,3,14,5,15,11] for more applications and results on LP-type problems, as well as e. g. [21,12,10,18] for the investigation of other, related frameworks.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Matoušek¹,

Škovroň²

2007

Theory of Comput.

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Many geometric algorithms are formulated for input objects in general position; sometimes this is for convenience and simplicity, and sometimes it is essential for the algorithm to work at all. For arbitrary inputs this requires removing degeneracies, which has usually been solved by relatively complicated and computationally demanding perturbation methods. The result of this paper can be regarded as an indication that the problem of removing degeneracies has no simple "abstract" solution. We consider LP-type problems, a successful axiomatic framework for optimization problems capturing, e. g., linear programming and the smallest enclosing ball of a point set. For infinitely many integers D we construct a Ddimensional LP-type problem such that in order to remove degeneracies from it, we have to increase the dimension to at least (1 + ε)D, where ε > 0 is an absolute constant. The proof consists of showing that certain posets cannot be covered by pairwise disjoint copies of Boolean algebras under some restrictions on their placement. To this end, we prove that certain systems of linear inequalities are unsolvable, which seems to require surprisingly precise calculations.

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The smallest enclosing ball of balls

Cited by 6 publications

References 0 publications

CaverDock: A Novel Method for the Fast Analysis of Ligand Transport

CaverDock: A Novel Method for the Fast Analysis of Ligand Transport

Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension

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