Algorithmic Graph Theory Qmul
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Algorithmic Techniques for the Polymer Sciences
This new book—the first of its kind—examines the use of algorithmic techniques to compress random and non-random sequential strings found in chains of polymers. The book is an introduction to algorithmic complexity. Examples taken from current research in the polymer sciences are used for compression of like-natured properties as found on a chain of polymers. Both theory and applied aspects of algorithmic compression are reviewed. A description of the types of polymers and their uses is followed by a chapter on various types of compression systems that can be used to compress polymer chains into manageable units. The work is intended for graduate and postgraduate university students in the physical sciences and engineering.
Topics in Algebraic Graph Theory
Author: Lowell W. Beineke
language: en
Publisher: Cambridge University Press
Release Date: 2004-10-04
There is no other book with such a wide scope of both areas of algebraic graph theory.
On Graph Isomorphism and the PageRank Algorithm
Graphs express relationships among objects, such as the radio connectivity among nodes in unmanned vehicle swarms. Some applications may rank a swarm's nodes by their relative importance, for example, using the PageRank algorithm applied in certain search engines to order query responses. The PageRank values of the nodes correspond to a unique eigenvector that can be computed using the power method, an iterative technique based on matrix multiplication. The first result is a practical lower bound on the PageRank algorithm's execution time that is derived by applying assumptions to the PageRank perturbation's scaling value and the PageRank vector's required numerical precision. The second result establishes nodes contained in the same block of the graph's coarsest equitable partition must have equal PageRank values. The third result, the AverageRank algorithm, ensures such nodes are assigned equal PageRank values. The fourth result, the ProductRank algorithm, reduces the time needed to find the PageRank vector by eliminating certain dot products in the power method if the graph's coarsest equitable partition contains blocks composed of multiple vertices. The fifth result, the QuotientRank algorithm, uses a quotient matrix induced by the coarsest equitable partition to further reduce the time needed to compute a swarm's PageRank vector.