Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 22 for “"combinatorial structures"”.
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Geometric and Combinatorial Structures on Graphs
In dieser Arbeit beschäftigen wir uns mit vier verschiedenen Themen: Zusammenhänge zwischen Schnyder-Wäldern und orthogonalen Flächen, die Anzahl planarer Orientierungen mit vorgegeben Ausgraden, aufspannende Bäume mit vielen Blättern und kleine ganzzahlige Realisierungen von Stapelpolytopen. Das …
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Combinatorial structures of hyperelliptic Hodge integrals
This dissertation explores the combinatorial structures that underlie hyperelliptic Hodge integrals. In order to compute hyperelliptic Hodge integrals, we use Atiyah-Bott (torus) localization on a stack of stable maps to [P1/Z2] = P1 × BZ2. The dissertation culminates in two results: a closed-form …
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Optimization on products of combinatorial structures
We consider optimization problems on combinatorial structures with a product form. The independence number of a graph G, denoted $\alpha (G)$, is the size of the largest independent set in G, where a subset S of the vertex set V(G) is independent if no two vertices in S are adjacent in G. The …
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Extremal problems on counting combinatorial structures
The fast developing field of extremal combinatorics provides a diverse spectrum of powerful tools with many applications to economics, computer science, and optimization theory. In this thesis, we focus on counting and coloring problems in this field. The complete balanced bipartite graph on $n$ …
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Combinatorial structures in online and convex optimization
… we consider three fundamental questions over combinatorial polytopes. First, we study the minimization of separable strictly convex functions over polyhedra. This problem is motivated by first-order optimization methods whose bottleneck relies on the minimization of a (often) separable, convex …
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Combinatorial structures and filter design in information spaces
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-03-18T15:56:28Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Jingjin.Yu.Thesis.pdf: 5836747 bytes, checksum: 3eb6d3859f8759ae7f5b8aea14208ae1 (MD5)
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Algorithms and algorithmic obstacles for probabilistic combinatorial structures
… average-case (approximation) algorithms for combinatorial optimization problems, as well as explore the algorithmic obstacles for a variety of discrete optimization problems arising in the theory of random graphs, statistics and machine learning. In particular, we consider the average-case …
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Efficient Machine Learning with High Order and Combinatorial Structures
… that exhibit complex and non-local dependency structures. There are three parts to this thesis. In the first part, we develop a toolbox of high order potentials (HOPs) that are useful for defining interactions and constraints that would be inefficient or otherwise difficult to use within the …
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Formalising Combinatorial Structures and Proof Techniques in Isabelle/HOL
… presents the first formalisations of numerous combinatorial structures and generalised formal proof techniques for combinatorics using the proof assistant Isabelle/HOL. These, in turn, explore the interplay between different mathematical fields in a formal environment. The thesis begins with an …
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Erasure-Correcting Codes Derived From Sudoku & Related Combinatorial Structures
… of an investigation into the use of puzzle-based combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the well-known number placement puzzle Sudoku and a novel three component construction designed specifically with puzzle-based …
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Algorithms and Algorithmic Barriers in High-Dimensional Statistics and Random Combinatorial Structures
… problems arising from the study of random combinatorial structures and of neural network models, with a particular emphasis on computational aspects. Our main contributions are summarized as follows. 1. Our first focus is on two algorithmic problems arising from the study of random …
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Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes
… Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the …
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Combinatorial properties of shifted complexes
… of shifted complexes and connections to various combinatorial structures.
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Parametric approaches to fractional programs: Analytical and empirical study
… dissertation, I focus on the linear fractional combinatorial optimization problem, a special case of fractional programming where all functions in the objective function and constraints are linear and all variables are binary that model certain combinatorial structures. Two parametric algorithms …
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Efficient Algorithms for High-Dimensional Data-Driven Sequential Decision-Making
… problems, each subject to a distinct \textit{combinatorial constraint} on its decisions: optimal stopping, sequential decision-making with limited moves and online bipartite max weight independent set. Assuming sample access to the underlying model (analogous to a \textit{generative model} in …
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Critical sets of full Latin squares
… sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes. In Chapter 3 we study known results on designs and the analogies between critical sets of the full n-Latin square and minimal defining sets of the …
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Hyperovals, Laguerre planes and hemisystems - an approach via symmetry
… hemisystems is due to their connection to other combinatorial structures, such as strongly regular graphs, partial quadrangles, and association schemes. In 2005, Cossidente and Penttila constructed a family of hemisystems in H(3,q2), q odd, and in 2009, the same authors constructed a family of …
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Coloring problems in combinatorics and descriptive set theory
… we study problems related to colorings of combinatorial structures both in the “classical” finite context and in the framework of descriptive set theory, with applications to topological dynamics and ergodic theory. This work consists of two parts, each of which is in turn split into a …
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Codes, graphs and designs related to iterated line graphs of complete graphs
… closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, Rn also has what we have termed as 6-cycle designs. These are designs in which the point set …
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Machine learning and combinatorial methods for discrete optimization problems
Combinatorial optimization is a central field of discrete mathematics, concerned with finding optimal solutions to problems over combinatorial structures such as graphs or set systems. However, while classical combinatorial optimization assumes complete knowledge of all problem parameters, …
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