Efficient Algorithm for Testing Structure Freeness of Finite Set of Biomolecular Sequences

The three-dimensional [Formula: see text]-shape is based on a mathematical formalism which determines exact relationships between points and shapes. It reconstructs surface and volume and detects 3D dot patterns for a given point cloud. [Formula: see text]-shape of a set of points is a sub-complex of Delaunay triangulation of this set. It generates a family of shapes according to the selected [Formula: see text] (a set of points). A method to compute the positions of the points of [Formula: see text] is proposed. These points are selected from the vertices of Voronoi diagram by analyzing the form of the polytopes; their elongation. This method allows the [Formula: see text]-shape to reflect different levels of detail in different parts of space. An efficient algorithm computing the three-dimensional [Formula: see text]-shape is presented, the [Formula: see text]-shape of a set of points is derived from the Delaunay triangulation of the same set. The speed of the algorithm is determined by the speed of the algorithm computing the Delaunay triangulation.

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Paths, Trees, and Flowers

Canadian Journal of Mathematics ◽

10.4153/cjm-1965-045-4 ◽

1965 ◽

Vol 17 ◽

pp. 449-467 ◽

Cited By ~ 1504

Author(s):

Jack Edmonds

Keyword(s):

Efficient Algorithm ◽

Maximum Cardinality ◽

End Points ◽

Finite Set

A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An edge is said to join its end-points.A matching in G is a subset of its edges such that no two meet the same vertex. We describe an efficient algorithm for finding in a given graph a matching of maximum cardinality. This problem was posed and partly solved by C. Berge; see Sections 3.7 and 3.8.

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

1996 ◽

Vol 54 ◽

pp. 440-441

Author(s):

P.J. Phillips ◽

J. Huang ◽

S. M. Dunn

Keyword(s):

Planar Graph ◽

Efficient Algorithm ◽

Spatial Organization ◽

Spatial Arrangement ◽

Stereo Image ◽

Image Model ◽

Geometric Invariants ◽

Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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