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 43 for “"Matroid"”.
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Ramsey Theory Using Matroid Minors
… a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified …
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Capturing elements in matroid minors
… dissertation, we begin with an introduction to a matroid as the natural generalization of independence arising in three different fields of mathematics. In the first chapter, we develop graph theory and matroid theory terminology necessary to the topic of this dissertation. In Chapter 2 and …
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Selected Problems on Matroid Minors
This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and …
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The linear matroid parity problem
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.
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The homotopy type of the matroid Grassmannian
… I establish a homotopy equivalence between the matroid Grassmannian [parallel] MacP(k, n) [parallel] and the real Grassmannian G(k, n) of k-planes in [Real set]n. This is accomplished by finding a Schubert stratification of the former space and analyzing its relationship to the ordinary Schubert …
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Matroid prophet inequalities and Bayesian mechanism design
… to make more than one selection, subject to a matroid constraint. We show that the gambler can still achieve at least half as much reward as the prophet; this result is the best possible, since it is known that the ratio cannot be improved even in the original prophet inequality, which …
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Theory and applications of freedom in matroids
To each cell e in a matroid M we can associate a non-negative integer ǁ e ǁ called the freedom of e. Geometrically the value ǁ e ǁ indicates how freely placed the cell is in the matroid. We see that ǁ e ǁ is equal to the degree of the modular cut generated by all the fully-dependent flats of M …
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Applications of Powerset Operators, Especially to Matroids
… the ``orthogonal complement'' operator.</p><p>In matroid theory, the orthogonal complement of a matroid \(M\) is also well-defined and similarly results in another matroid. Although this new matroid is more commonly referred to as the `dual matroid', denoted as \(M^*\), and typically formed using …
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Bicircular Matroids with Circuits of at Most Two Sizes
Young in his paper titled, Matroid Designs in 1973, reports that Murty in his paper titled, Equicardinal Matroids and Finite Geometries in 1968, was the first to study matroids with all hyperplanes having the same size. Murty called such a matroid an ``Equicardinal Matroid''. Young renamed such a …
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The Characterization Of Graphs With Small Bicycle Spectrum
Matroids designs are defined to be matroids in which the hyperplanes all have the same size. The dual of a matroid design is a matroid with all circuits of the same size, called a dual matroid design. The connected bicircular dual matroid designs have been characterized previously. In addition, …
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A Dual Fano, and Dual Non-Fano Matroidal Network
<p>Matroidal networks are useful tools in furthering research in network coding. They have been used to show the limitations of linear coding solutions. In this paper we examine the basic information on network coding and matroid theory. We then go over the method of creating matroidal networks. …
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The structure of 4-separations in 4-connected matroids
… described a tree decomposition for a 3-connected matroid M that displays, up to a natural equivalence, all non-trivial 3-separations of M. Crossing 3-separations gave rise to fundamental structures known as flowers. In this dissertation, we define generalized flower structure called a k-flower, …
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Classification and enumeration of special classes of posets and polytopes
… In the second topic concerns lattice path matroid polytopes. The theory of matroid polytopes has gained prominence due to its applications in algebraic geometry, combinatorial optimization, Coxeter group theory, and, most recently, tropical geometry. In general matroid polytopes are not …
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Regular Round Matroids
<p>A matroid <em>M</em> is a finite set <em>E</em>, called the ground set of <em>M</em>, together with a notion of what it means for subsets of <em>E</em> to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors …
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Matchings, matroids and submodular functions
… optimization: non-bipartite matching, matroid intersection, and submodular function minimization. We develop simple, efficient, randomized algorithms for the first two problems, and prove new lower bounds for the last two problems. For the matching problem, we give an algorithm for …
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Maximum-Sized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7
Let M be the class of simple matroids which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find …
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Combinatorial aspects of total positivity
… a notion of total positivity for oriented matroids. Namely, I introduce the positive Bergman complex of an oriented matroid, which is a matroidal analogue of a positive tropical variety. I prove that this object is homeomorphic to a ball, and relate it to the Las Vergnas face lattice of an …
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Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices
… lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of subdivisions of lattice polytopes, and how they can be used to address algebraic questions. Chapter two discusses tropical hyperplane arrangements and the tropical …
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Subset Selection via Spectral Objectives
… to subsets S that are bases of a specific matroid. This will allow us to model a much broader class of problems. This work focuses on four problems which can be modeled in the spectral subset selection framework. The first, is determinant maximization under matroid constraints. For this …
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Contributions on secretary problems, independent sets of rectangles and related problems
… combinatorial optimization. We first study the matroid secretary problem, which is a generalization proposed by Babaioff, Immorlica and Kleinberg of the classical secretary problem. In this problem, the elements of a given matroid are revealed one by one. When an element is revealed, we learn …
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