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Full-Text Articles in Physical Sciences and Mathematics
The Pc-Tree Algorithm, Kuratowski Subdivisions, And The Torus., Charles J. Suer
The Pc-Tree Algorithm, Kuratowski Subdivisions, And The Torus., Charles J. Suer
Electronic Theses and Dissertations
The PC-Tree algorithm of Shih and Hsu (1999) is a practical linear-time planarity algorithm that provides a plane embedding of the given graph if it is planar and a Kuratowski subdivision otherwise. Remarkably, there is no known linear-time algorithm for embedding graphs on the torus. We extend the PC-Tree algorithm to a practical, linear-time toroidality test for K3;3-free graphs called the PCK-Tree algorithm. We also prove that it is NP-complete to decide whether the edges of a graph can be covered with two Kuratowski subdivisions. This greatly reduces the possibility of a polynomial-time toroidality testing algorithm based solely on edge-coverings …
Optcluster : An R Package For Determining The Optimal Clustering Algorithm And Optimal Number Of Clusters., Michael N. Sekula
Optcluster : An R Package For Determining The Optimal Clustering Algorithm And Optimal Number Of Clusters., Michael N. Sekula
Electronic Theses and Dissertations
Determining the best clustering algorithm and ideal number of clusters for a particular dataset is a fundamental difficulty in unsupervised clustering analysis. In biological research, data generated from Next Generation Sequencing technology and microarray gene expression data are becoming more and more common, so new tools and resources are needed to group such high dimensional data using clustering analysis. Different clustering algorithms can group data very differently. Therefore, there is a need to determine the best groupings in a given dataset using the most suitable clustering algorithm for that data. This paper presents the R package optCluster as an efficient …