The PR-tree data structure is introduced to characterize the sets of path-tree models of path graphs. We further characterize the sets of directed path-tree models of directed path graphs with a slightly restricted form of the PR-tree called the Strong PR-tree. Additionally, via PR-trees and Strong PR-trees, we characterize path graphs and directed path graphs by their Split Decompositions. Two distinct approaches (Split Decomposition and Reduction) are presented to construct a PR-tree that captures the path-tree models of a given graph G = (V, E) with n = |V| and m = |E|. An implementation of the split decomposition approach is presented which runs in O(nm) time. Similarly, an implementation of the reduction approach is presented which runs in O(A(n + m)nm) time (where A(s) is the inverse of Ackermann’s function arising from Union-Find [40]). Also, from a PR-tree, an algorithm to construct a corresponding Strong PR-tree is given which runs in O(n + m) time. The sizes of the PR-trees and Strong PR-trees produced by these approaches are O(n + m) with respect to the given graph. Furthermore, we demonstrate that an implicit form of the PR-tree and Strong PR-tree can be represented in O(n) space.

The PR-tree data structure is introduced to characterize the sets of path-tree models of path graphs. We further characterize the sets of directed path-tree models of directed path graphs with a slightly restricted form of the PR-tree called the Strong PR-tree. Additionally, via PR-trees and Strong PR-trees, we characterize path graphs and directed path graphs by their Split Decompositions. Two distinct approaches (Split Decomposition and Reduction) are presented to construct a PR-tree that captures the path-tree models of a given graph G = (V, E) with n = |V| and m = |E|. An implementation of the split decomposition approach is presented which runs in O(nm) time. Similarly, an implementation of the reduction approach is presented which runs in O(A(n + m)nm) time (where A(s) is the inverse of Ackermann’s function arising from Union-Find [40]). Also, from a PR-tree, an algorithm to construct a corresponding Strong PR-tree is given which runs in O(n + m) time. The sizes of the PR-trees and Strong PR-trees produced by these approaches are O(n + m) with respect to the given graph. Furthermore, we demonstrate that an implicit form of the PR-tree and Strong PR-tree can be represented in O(n) space.

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, August 2003. / Includes bibliographical references. Also available on the Internet.

This report introduces ProGENitor; a system to empower individuals with career advice based on vast amounts of data. Specifically, it develops a machine learning algorithm that shows users how to efficiently reached specific career goals based upon the histories of other users. A reference implementation of this algorithm is presented, along with experimental results that show that it provides quality actionable intelligence to users. / text

published_or_final_version / abstract / toc / Computer Science / Master / Master of Philosophy

published_or_final_version / Computer Science / Master / Master of Philosophy

Reconstruction results attempt to rebuild polygons from visibility information. Reconstruction of a general polygon from its visibility graph is still open and only known to be in PSPACE; thus additional information, such as the ordering of the edges around nodes that corresponds to the order of the visibilities around vertices is frequently added. The first section of this thesis extracts, in o(E) time, the Hamiltonian cycle that corresponds to the boundary of the polygon from the polygon's ordered visibility graph. Also, it converts an unordered visibility graph and Hamiltonian cycle to the ordered visibility graph for that polygon in O(E) time. The secod, and major result is an algorithm to reconstruct an arthogonal polygon that is consistent with the Hamiltonian cylce and visibility stabs of the sides of an unknown polygon. The algorithm uses O(nlogn) time, assuming there are no collinear sides, and )(n2) time otherwise. / vii, 78 leaves ; 28 cm.

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