Physical Sciences and Mathematics Commons^™

Novel Monte Carlo Methods For Large-Scale Linear Algebra Operations, Hao Ji

Computer Science Theses & Dissertations

Linear algebra operations play an important role in scientific computing and data analysis. With increasing data volume and complexity in the "Big Data" era, linear algebra operations are important tools to process massive datasets. On one hand, the advent of modern high-performance computing architectures with increasing computing power has greatly enhanced our capability to deal with a large volume of data. One the other hand, many classical, deterministic numerical linear algebra algorithms have difficulty to scale to handle large data sets.

Monte Carlo methods, which are based on statistical sampling, exhibit many attractive properties in dealing with large volume of …

Indifference Graphs And The Single Row Routing Problem, Peter J. Looges

Computer Science Theses & Dissertations

This thesis investigates the subclass of interval graphs known as indifference graphs. New optimal algorithms for recognition, center, diameter, maximum matching, Hamiltonian path and domination in indifference graphs are presented. The recognition algorithm produces a linear order with properties which allow the solution of the other problems in linear time. Indifference graphs are further applied to the single row routing problem which results in both sequential,. and parallel routing algorithms.