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Full-Text Articles in Physical Sciences and Mathematics
The Maximum Clique Problem: Algorithms, Applications, And Implementations, John David Eblen
The Maximum Clique Problem: Algorithms, Applications, And Implementations, John David Eblen
Doctoral Dissertations
Computationally hard problems are routinely encountered during the course of solving practical problems. This is commonly dealt with by settling for less than optimal solutions, through the use of heuristics or approximation algorithms. This dissertation examines the alternate possibility of solving such problems exactly, through a detailed study of one particular problem, the maximum clique problem. It discusses algorithms, implementations, and the application of maximum clique results to real-world problems. First, the theoretical roots of the algorithmic method employed are discussed. Then a practical approach is described, which separates out important algorithmic decisions so that the algorithm can be easily …
Computational Circle Packing: Geometry And Discrete Analytic Function Theory, Gerald Lee Orick
Computational Circle Packing: Geometry And Discrete Analytic Function Theory, Gerald Lee Orick
Doctoral Dissertations
Geometric Circle Packings are of interest not only for their aesthetic appeal but also their relation to discrete analytic function theory. This thesis presents new computational methods which enable additional practical applications for circle packing geometry along with providing a new discrete analytic interpretation of the classical Schwarzian derivative and traditional univalence criterion of classical analytic function theory. To this end I present a new method of computing the maximal packing and solving the circle packing layout problem for a simplicial 2-complex along with additional geometric variants and applications. This thesis also presents a geometric discrete Schwarzian quantity whose value …