Topics in exact precision mathematical programming

The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.Ph.D.Committee Chair: Dr. William J. Cook; Committee Member: Dr. George Nemhauser; Committee Member: Dr. Robin Thomas; Committee Member: Dr. Santanu Dey; Committee Member: Dr. Shabbir Ahmed; Committee Member: Dr. Zonghao G

The Nornir run-time system for parallel programs using Kahn process networks on multi-core machines – A flexible alternative to MapReduce

Even though shared-memory concurrency is a paradigm frequently used for developing parallel applications on small- and middle-sized machines, experience has shown that it is hard to use. This is largely caused by synchronization primitives which are low-level, inherently non-deterministic, and, consequently, non-intuitive to use. In this paper, we present the Nornir run-time system. Nornir is comparable to well-known frameworks such as MapReduce and Dryad that are recognized for their efficiency and simplicity. Unlike these frameworks, Nornir also supports process structures containing branches and cycles. Nornir is based on the formalism of Kahn process networks, which is a shared-nothing, message-passing model of concurrency. We deem this model a simple and deterministic alternative to shared-memory concurrency. Experiments with real and synthetic benchmarks on up to 8 CPUs show that performance in most cases scales almost linearly with the number of CPUs, when not limited by data dependencies. We also show that the modeling flexibility allows Nornir to outperform its MapReduce counterparts using well-known benchmarks. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited

Graph theory in America 1876-1950

This narrative is a history of the contributions made to graph theory in the United States of America by American mathematicians and others who supported the growth of scholarship in that country, between the years 1876 and 1950. The beginning of this period coincided with the opening of the first research university in the United States of America, The Johns Hopkins University (although undergraduates were also taught), providing the facilities and impetus for the development of new ideas. The hiring, from England, of one of the foremost mathematicians of the time provided the necessary motivation for research and development for a new generation of American scholars. In addition, it was at this time that home-grown research mathematicians were first coming to prominence. At the beginning of the twentieth century European interest in graph theory, and to some extent the four-colour problem, began to wane. Over three decades, American mathematicians took up this field of study - notably, Oswald Veblen, George Birkhoff, Philip Franklin, and Hassler Whitney. It is necessary to stress that these four mathematicians and all the other scholars mentioned in this history were not just graph theorists but worked in many other disciplines. Indeed, they not only made significant contributions to diverse fields but, in some cases, they created those fields themselves and set the standards for others to follow. Moreover, whilst they made considerable contributions to graph theory in general, two of them developed important ideas in connection with the four-colour problem. Grounded in a paper by Alfred Bray Kempe that was notorious for its fallacious 'proof' of the four-colour theorem, these ideas were the concepts of an unavoidable set and a reducible configuration. To place the story of these scholars within the history of mathematics, America, and graph theory, brief accounts are presented of the early years of graph theory, the early years of mathematics and graph theory in the USA, and the effects of the founding of the first institute for postgraduate study in America. Additionally, information has been included on other influences by such global events as the two world wars, the depression, the influx of European scholars into the United States of America, mainly during the 1930s, and the parallel development of graph theory in Europe. Until the end of the nineteenth century, graph theory had been almost entirely the prerogative of European mathematicians. Perhaps the first work in graph theory carried out in America was by Charles Sanders Peirce, arguably America's greatest logician and philosopher at the time. In the 1860s, he studied the four-colour conjecture and claimed to have written at least two papers on the subject during that decade, but unfortunately neither of these has survived. William Edward Story entered the field in 1879, with unfortunate consequences, but it was not until 1897 that an American mathematician presented a lecture on the subject, albeit only to have the paper disappear. Paul Wernicke presented a lecture on the four-colour problem to the American Mathematician Society, but again the paper has not survived. However, his 1904 paper has survived and added to the story of graph theory, and particularly the four-colour conjecture. The year 1912 saw the real beginning of American graph theory with Veblen and Birkhoff publishing major contributions to the subject. It was around this time that European mathematicians appeared to lose interest in graph theory. In the period 1912 to 1950 much of the progress made in the subject was from America and by 1950 not only had the United States of America become the foremost country for mathematics, it was the leading centre for graph theory

Knowledge Extraction from Textual Resources through Semantic Web Tools and Advanced Machine Learning Algorithms for Applications in Various Domains

Nowadays there is a tremendous amount of unstructured data, often represented by texts, which is created and stored in variety of forms in many domains such as patients' health records, social networks comments, scientific publications, and so on. This volume of data represents an invaluable source of knowledge, but unfortunately it is challenging its mining for machines. At the same time, novel tools as well as advanced methodologies have been introduced in several domains, improving the efficacy and the efficiency of data-based services. Following this trend, this thesis shows how to parse data from text with Semantic Web based tools, feed data into Machine Learning methodologies, and produce services or resources to facilitate the execution of some tasks. More precisely, the use of Semantic Web technologies powered by Machine Learning algorithms has been investigated in the Healthcare and E-Learning domains through not yet experimented methodologies. Furthermore, this thesis investigates the use of some state-of-the-art tools to move data from texts to graphs for representing the knowledge contained in scientific literature. Finally, the use of a Semantic Web ontology and novel heuristics to detect insights from biological data in form of graph are presented. The thesis contributes to the scientific literature in terms of results and resources. Most of the material presented in this thesis derives from research papers published in international journals or conference proceedings