Дисертації з теми "Structural Combinatorics"
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Ferra, Gomes de Almeida Girão António José. "Extremal and structural problems of graphs." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/285427.
Повний текст джерелаBorenstein, Evan. "Additive stucture, rich lines, and exponential set-expansion." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29664.
Повний текст джерелаCommittee Chair: Croot, Ernie; Committee Member: Costello, Kevin; Committee Member: Lyall, Neil; Committee Member: Tetali, Prasad; Committee Member: Yu, XingXing. Part of the SMARTech Electronic Thesis and Dissertation Collection.
Tanigawa, Shinichi. "Combinatorial Rigidity and Generation of Discrete Structures." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120806.
Повний текст джерелаBrignall, Robert. "Simplicity in relational structures and its application to permutation classes." Thesis, St Andrews, 2007. http://hdl.handle.net/10023/431.
Повний текст джерелаRockney, Alissa Ann. "A Predictive Model Which Uses Descriptors of RNA Secondary Structures Derived from Graph Theory." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etd/1300.
Повний текст джерелаAmiouny, Samir V. "Combinatorial mechanics." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/25576.
Повний текст джерелаBarnard, Kristen M. "Some Take-Away Games on Discrete Structures." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/44.
Повний текст джерелаAllen, Peter. "Finding combinatorial structures." Thesis, London School of Economics and Political Science (University of London), 2008. http://etheses.lse.ac.uk/60/.
Повний текст джерелаSpiegel, Christoph. "Additive structures and randomness in combinatorics." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669327.
Повний текст джерелаLa combinatòria aritmètica, la teoria combinatòria dels nombres, la teoria additiva estructural i la teoria additiva de nombres són alguns dels termes que es fan servir per descriure una branca extensa i activa que es troba en la intersecció de la teoria de nombres i de la combinatòria, i que serà el motiu d'aquesta tesi doctoral. La primera part tracta la qüestió de sota quines circumstàncies es solen produir solucions a sistemes lineals d’equacions arbitràries en estructures additives. Una primera pregunta que s'estudia es refereix al punt en que conjunts d’una mida determinada contindran normalment una solució. Establirem un llindar i estudiarem també la distribució del nombre de solucions en aquest llindar, tot demostrant que en certs casos aquesta distribució convergeix a una distribució de Poisson. El següent tema de la tesis es relaciona amb el teorema de Van der Waerden, que afirma que cada coloració finita dels nombres enters conté una progressió aritmètica monocromàtica de longitud arbitrària. Aquest es considera el primer resultat en la teoria de Ramsey. Rado va generalitzar el resultat de van der Waerden tot caracteritzant en aquells sistemes lineals les solucions de les quals satisfan una propietat similar i Szemerédi la va reforçar amb una versió de densitat del resultat. Centrarem la nostra atenció cap a versions del teorema de Rado i Szemerédi en conjunts aleatoris, ampliant els treballs anteriors de Friedgut, Rödl, Rucinski i Schacht i de Conlon, Gowers i Schacht. Per últim, Chvátal i Erdos van suggerir estudiar estudiar jocs posicionals del tipus Maker-Breaker. Aquests jocs tenen una connexió profunda amb la teoria de les estructures aleatòries i ens basarem en el treball de Bednarska i Luczak per establir el llindar de la quantitat que necessitem per analitzar una gran varietat de jocs en favor del segon jugador. S'inclouen jocs en què el primer jugador vol ocupar una solució d'un sistema lineal d'equacions donat, generalitzant els jocs de van der Waerden introduïts per Beck. La segona part de la tesis tracta sobre el comportament extrem dels conjunts amb propietats additives interessants. Primer, considerarem els conjunts de Sidon, és a dir, conjunts d’enters amb diferències úniques quan es consideren parelles d'elements. Estudiarem una generalització dels conjunts de Sidons proposats recentment per Kohayakawa, Lee, Moreira i Rödl, en que les diferències entre parelles no són només diferents, sinó que, en realitat, estan allunyades una certa proporció en relació a l'element més gran. Obtindrem límits més baixos per a conjunts infinits que els obtinguts pels anteriors autors tot usant una construcció de conjunts de Sidon infinits deguda a Cilleruelo. Com a conseqüència d'aquests límits, obtindrem també el millor límit inferior actual per als conjunts de Sidon en conjunts infinits generats aleatòriament de nombres enters d'alta densitat. A continuació, un dels resultats centrals a la intersecció de la combinatòria i la teoria dels nombres és el teorema de Freiman-Ruzsa, que afirma que el conjunt suma d'un conjunt finit d’enters donats pot ser cobert de manera eficient per una progressió aritmètica generalitzada. En el cas de que el conjunt suma sigui de mida petita, existeixen descripcions estructurals més precises. Primer estudiarem els resultats que van més enllà del conegut teorema de Freiman 3k-4 en els enters. Llavors veurem una aplicació d’aquests resultats a conjunts de dobles petits en grups cíclics finits. Finalment, dirigirem l’atenció cap a conjunts amb funcions de representació gairebé constants. Erdos i Fuchs van establir que les funcions de representació de conjunts arbitraris d’enters no poden estar massa a prop de ser constants. Primer estendrem el resultat d’Erdos i Fuchs a funcions de representació ordenades. A continuació, abordarem una pregunta relacionada de Sárközy i Sós sobre funció de representació ponderada.
Burris, Christina Suzann. "Analytic Combinatorics Applied to RNA Structures." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83888.
Повний текст джерелаMaster of Science
Ribonucleic acid (RNA), similar in composition to well-known DNA, plays a myriad of roles within the cell. The major distinction between DNA and RNA is the nature of the nucleotide pairings. RNA is single stranded, to mean that its nucleotides are paired with one another (as opposed to a unique complementary strand). Consequently, RNA exhibits a knotted 3D structure. These diverse structures (folding patterns) have been shown to play important roles in RNA function, likened to a lock and key system. Given the cost of gathering data on folding patterns, little is known about exactly how structure and function are related. The work presented centers around building the mathematical framework of RNA structures in an effort to guide technology and further scientific discovery. We provide insight into the prevalence of certain important folding patterns.
Roberts, Barnaby. "Structure and randomness in extremal combinatorics." Thesis, London School of Economics and Political Science (University of London), 2017. http://etheses.lse.ac.uk/3592/.
Повний текст джерелаPatel, Viresh. "Partitions of combinatorial structures." Thesis, London School of Economics and Political Science (University of London), 2009. http://etheses.lse.ac.uk/3006/.
Повний текст джерелаDovgal, Sergey. "An interdisciplinary image of Analytic Combinatorics." Thesis, Paris 13, 2019. http://www.theses.fr/2019PA131065.
Повний текст джерелаThis thesis is devoted to the development of tools and the use of methods from Analytic Combinatorics, including exact and asymptotic enumeration, statistical properties of random objects, and random generation.The key ingredient is the multidisciplinarity of the domain, which is emphasised by using examples from computational logic, statistical mechanics, biology, mathematical statistics, networks and queueing theory
Da, Silva Pereira Luis Miguel. "Combinatorics of Singular Cardinals and PCF structures." Paris 7, 2007. http://www.theses.fr/2007PA077100.
Повний текст джерелаThis work is centered on Shelah's PCF theory. We study the connection between the topology of PCF spaces and standard PCF theory notions. We prove a generalization of the result that says that separable PCF spaces are sequential and obtain as a corollary that there exist many sequences that have true cofinality modulo the ideal of finite sets. We prove that this corollary is optimal. We also give a topological proof of cardinal estimates previously obtained through the use of the Galvin-Hajnal norm. We study a consequence of the negation of Shelah's PCF conjecture called the Approachable Free Subset Property (AFSP). We note that AFSP is incompatible with the existence of tree-like continuous scales and prove the consistency of these scales with the largest large cardinal axioms thus establishing that AFSP is not implied by large cardinals. We study the existence of tree-like continuous scales and the negation of AFSP in several Prikry extensions of the universe
Hamel, Mariah. "Arithmetic structures in random sets." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2838.
Повний текст джерелаMcShine, Lisa Maria. "Random sampling of combinatorial structures." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28771.
Повний текст джерелаFalgas-Ravry, Victor. "Thresholds in probabilistic and extremal combinatorics." Thesis, Queen Mary, University of London, 2012. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8827.
Повний текст джерелаOkoth, Isaac Owino. "Combinatorics of oriented trees and tree-like structures." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96860.
Повний текст джерелаENGLISH ABSTRACT : In this thesis, a number of combinatorial objects are enumerated. Du and Yin as well as Shin and Zeng (by a different approach) proved an elegant formula for the number of labelled trees with respect to a given in degree sequence, where each edge is oriented from a vertex of lower label towards a vertex of higher label. We refine their result to also take the number of sources (vertices of in degree 0) or sinks (vertices of out degree 0) into account. We find formulas for the mean and variance of the number of sinks or sources in these trees. We also obtain a differential equation and a functional equation satisfied by the generating function for these trees. Analogous results for labelled trees with two marked vertices, related to functional digraphs, are also established. We extend the work to count reachable vertices, sinks and leaf sinks in these trees. Among other results, we obtain a counting formula for the number of labelled trees on n vertices in which exactly k vertices are reachable from a given vertex v and also the average number of vertices that are reachable from a specified vertex in labelled trees of order n. In this dissertation, we also enumerate certain families of set partitions and related tree-like structures. We provide a proof for a formula that counts connected cycle-free families of k set partitions of {1, . . . , n} satisfying a certain coherence condition and then establish a bijection between these families and the set of labelled free k-ary cacti with a given vertex-degree distribution. We then show that the formula also counts coloured Husimi graphs in which there are no blocks of the same colour that are incident to one another. We extend the work to count coloured oriented cacti and coloured cacti. Noncrossing trees and related tree-like structures are also considered in this thesis. Specifically, we establish formulas for locally oriented noncrossing trees with a given number of sources and sinks, and also with given indegree and outdegree sequences. The work is extended to obtain the average number of reachable vertices in these trees. We then generalise the concept of noncrossing trees to find formulas for the number of noncrossing Husimi graphs, cacti and oriented cacti. The study is further extended to find formulas for the number of bicoloured noncrossing Husimi graphs and the number of noncrossing connected cycle-free pairs of set partitions.
AFRIKAANSE OPSOMMING : In hierdie tesis word ’n aantal kombinatoriese objekte geenumereer. Du en Yin asook Shin en Zeng (deur middel van ’n ander benadering) het ’n elegante formule vir die aantal geëtiketteerde bome met betrekking tot ’n gegewe ingangsgraadry, waar elke lyn van die nodus met die kleiner etiket na die nodus met die groter etiket toe georiënteer word. Ons verfyn hul resultaat deur ook die aantal bronne (nodusse met ingangsgraad 0) en putte (nodusse met uitgangsgraad 0) in ag te neem. Ons vind formules vir die gemiddelde en variansie van die aantal putte of bronne in hierdie bome. Ons bepaal verder ’n differensiaalvergelyking en ’n funksionaalvergelyking wat deur die voortbringende funksie van hierdie bome bevredig word. Analoë resultate vir geëtiketteerde bome met twee gemerkte nodusse (wat verwant is aan funksionele digrafieke), is ook gevind. Ons gaan verder voort deur ook bereikbare nodusse, bronne en putte in hierdie bome at te tel. Onder andere verkry ons ’n formule vir die aantal geëtiketteerde bome met n nodusse waarin presies k nodusse vanaf ’n gegewe nodus v bereikbaar is asook die gemiddelde aantal nodusse wat bereikbaar is vanaf ’n gegewe nodus. Ons enumereer in hierdie tesis verder sekere families van versamelingsverdelings en soortgelyke boom-vormige strukture. Ons gee ’n bewys vir ’n formule wat die aantal van samehangende siklus-vrye families van k versamelingsverdelings op {1, . . . , n} wat ’n sekere koherensie-vereiste bevredig, en ons beskryf ’n bijeksie tussen hierdie familie en die versameling van geëtiketteerde vrye k-êre kaktusse met ’n gegewe nodus-graad-verdeling. Ons toon ook dat hierdie formule ook gekleurde Husimi-grafieke tel waar blokke van dieselfde kleur nie insident met mekaar mag wees nie. Ons tel verder ook gekleurde georiënteerde kaktusse en gekleurde kaktusse. Nie-kruisende bome en soortgelyke boom-vormige strukture word in hierdie tesis ook beskou. On bepaal spesifiek formules vir lokaal georiënteerde nie-kruisende bome wat ’n gegewe aantal bronne en putte het asook nie-kruisende bome met gegewe ingangs- en uitgangsgraadrye. Ons gaan voort deur die gemiddelde aantal bereikbare nodusse in hierdie bome te bepaal. Ons veralgemeen dan die konsep van nie-kruisende bome en vind formules vir die aantal nie-kruisende Husimi-grafieke, kaktusse en georiënteerde kaktusse. Laastens vind ons ’n formule vir die aantaal tweegekleurde nie-kruisende Husimi-grafieke en die aantal nie-kruisende samehangende siklus-vrye pare van versamelingsverdelings.
Delagrave, Simon. "Combinatorial structure and function studies." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/38736.
Повний текст джерелаFountoulakis, N. "Thresholds and the structure of sparse random graphs." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275502.
Повний текст джерелаLimnios, Stratis. "Graph Degeneracy Studies for Advanced Learning Methods on Graphs and Theoretical Results Edge degeneracy: Algorithmic and structural results Degeneracy Hierarchy Generator and Efficient Connectivity Degeneracy Algorithm A Degeneracy Framework for Graph Similarity Hcore-Init: Neural Network Initialization based on Graph Degeneracy." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX038.
Повний текст джерелаExtracting Meaningful substructures from graphs has always been a key part in graph studies. In machine learning frameworks, supervised or unsupervised, as well as in theoretical graph analysis, finding dense subgraphs and specific decompositions is primordial in many social and biological applications among many others.In this thesis we aim at studying graph degeneracy, starting from a theoretical point of view, and building upon our results to find the most suited decompositions for the tasks at hand.Hence the first part of the thesis we work on structural results in graphs with bounded edge admissibility, proving that such graphs can be reconstructed by aggregating graphs with almost-bounded-edge-degree. We also provide computational complexity guarantees for the different degeneracy decompositions, i.e. if they are NP-complete or polynomial, depending on the length of the paths on which the given degeneracy is defined.In the second part we unify the degeneracy and admissibility frameworks based on degree and connectivity. Within those frameworks we pick the most expressive, on the one hand, and computationally efficient on the other hand, namely the 1-edge-connectivity degeneracy, to experiment on standard degeneracy tasks, such as finding influential spreaders.Following the previous results that proved to perform poorly we go back to using the k-core but plugging it in a supervised framework, i.e. graph kernels. Thus providing a general framework named core-kernel, we use the k-core decomposition as a preprocessing step for the kernel and apply the latter on every subgraph obtained by the decomposition for comparison. We are able to achieve state-of-the-art performance on graph classification for a small computational cost trade-off.Finally we design a novel degree degeneracy framework for hypergraphs and simultaneously on bipartite graphs as they are hypergraphs incidence graph. This decomposition is then applied directly to pretrained neural network architectures as they induce bipartite graphs and use the coreness of the neurons to re-initialize the neural network weights. This framework not only outperforms state-of-the-art initialization techniques but is also applicable to any pair of layers convolutional and linear thus being applicable however needed to any type of architecture
Montejano, Cantoral Amanda. "Colored combinatorial structures: homomorphisms and counting." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/32031.
Повний текст джерелаStarting with the four color problem, the theory of graph coloring has existed for more than 150 years. It deals with the fundamental problem of partitioning a set of objects into classes according to certain rules. From this modest beginning, the theory has become central in discrete mathematics, with many contemporary generalizations and applications. In this thesis, our particular interest is in two very active areas of research which have emerged from coloring problems: Graph Homomorphism Theory and Arithmetic Ramsey Theory. Graph Homomorphism Theory can be described as the study of classes of combinatorial structures under natural morphisms. The chromatic number of a simple graph G can be stated, in this context, as the smallest complete graph to which G admits a homomorphism. Thus Graph Homomorphism Theory has been extensively studied as a generalization of colorings. An excellent reference in the subject is the book by Hell and Nesetril {Graphs and homomorphisms, Oxf. Univ. Press, 2004}. Ramsey Theory studies the existence of particular color patterns in colored structures. Starting with the Theorems of Ramsey, Hilbert, Schur and van der Waerden, the theory has developed as a wide and beautiful area of combinatorics, in which a great variety of techniques are used from many branches of mathematics. Many of the classical results in the area are arithmetic versions of the theory and we are interested in this particular branch of Ramsey Theory. A good reference in the area is the book of Langman and Robertson {Ramsey Theory on the Integers, Stud. Math. Lib. 24, AMS, 2003}. This thesis is organized in two parts. The first part deals with the study of homomorphisms in the class of colored mixed graphs, which are graphs with vertices linked by both colored arcs and colored edges. The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (color preserving) homomorphism from G to H. These notions were introduced by Nesetril and Raspaud in {Colored homomorphisms of colored mixed graphs, J. C. T. Ser. B 80 (2000)}. Generalizing known results for the class of oriented graphs we study the colored mixed chromatic number of paths, trees, graphs with bounded acyclic chromatic number, graphs of bounded treewidth, planar graphs, outerplanar graphs and sparse graphs. In particular we give the exact chormatic number of planar graphs and of partial 2-trees with appropriately large girth. Motivated by the dichotomy conjecture for relational structures we focuss on the class of 2-edge colored graphs and study its relationship with the class of oriented graphs. In particular we consider the characterization of cores and of duality pairs in this class. The second part of the thesis is related to Arithmetic Ramsey Theory. We consider the existence and the enumeration of colored structures, mainly monochromatic or rainbow structures, in colorings of finite groups. The structures under consideration can be described as solutions of systems of equations in the group, the main examples being arithmetic progressions and Schur triples. We give a structural description of those colorings in abelian groups which do not contain 3-term arithmetic progressions with its members having pairwise distinct colors. This structural description proves a conjecture of Jungic et al. {Rainbow Ramsey Theory. Integers: E. J. C. N. T. 5(2) A9. (2005)} on the size of the smallest chromatic class of such colorings in cyclic groups.
Stokes, Klara. "Combinatorial structures for anonymous database search." Doctoral thesis, Universitat Rovira i Virgili, 2011. http://hdl.handle.net/10803/52799.
Повний текст джерелаRattan, Amarpreet. "Parking Functions and Related Combinatorial Structures." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1028.
Повний текст джерелаTyomkyn, Mykhaylo. "Packings and embeddings of combinatorial structures." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609410.
Повний текст джерелаGoldberg, Leslie Ann. "Efficient algorithms for listing combinatorial structures." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/10917.
Повний текст джерелаAtminas, Aistis. "Well-quasi-ordering of combinatorial structures." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/67023/.
Повний текст джерелаLittle, David P. "Q-enumeration of classical combinatorial structures /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2000. http://wwwlib.umi.com/cr/ucsd/fullcit?p9989758.
Повний текст джерелаEmtander, Eric. "Chordal and Complete Structures in Combinatorics and Commutative Algebra." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-48241.
Повний текст джерелаMustafa, Nabil. "Approximations of Points: Combinatorics and Algorithms." Habilitation à diriger des recherches, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-01062825.
Повний текст джерелаLeung, Yiu-cho. "Counting combinatorial structures in recursively constructible graphs /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?CSED%202007%20LEUNG.
Повний текст джерелаQuinn, Kathleen Anne Sara. "Combinatorial structures with applications to information theory." Thesis, Royal Holloway, University of London, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.261791.
Повний текст джерелаGupta, Swati Ph D. Massachusetts Institute of Technology. "Combinatorial structures in online and convex optimization." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112014.
Повний текст джерелаThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 157-163).
Motivated by bottlenecks in algorithms across 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 metric, known as the Bregman divergence. We provide a conceptually simple algorithm, Inc-Fix, in the case of submodular base polyhedra. For cardinality-based submodular polytopes, we show that Inc-Fix can be speeded up to be the state-of-the-art method for minimizing uniform divergences. We show that the running time of Inc-Fix is independent of the convexity parameters of the objective function. The second question is concerned with the complexity of the parametric line search problem in the extended submodular polytope P: starting from a point inside P, how far can one move along a given direction while maintaining feasibility. This problem arises as a bottleneck in many algorithmic applications like the above-mentioned Inc-Fix algorithm and variants of the Frank-Wolfe method. One of the most natural approaches is to use the discrete Newton's method, however, no upper bound on the number of iterations for this method was known. We show a quadratic bound resulting in a factor of n6 reduction in the worst-case running time from the previous state-of-the-art. The analysis leads to interesting extremal questions on set systems and submodular functions. Next, we develop a general framework to simulate the well-known multiplicative weights update algorithm for online linear optimization over combinatorial strategies U in time polynomial in log /U/, using efficient approximate general counting oracles. We further show that efficient counting over the vertex set of any 0/1 polytope P implies efficient convex minimization over P. As a byproduct of this result, we can approximately decompose any point in a 0/1 polytope into a product distribution over its vertices. Finally, we compare the applicability and limitations of the above results in the context of finding Nash-equilibria in combinatorial two-player zero-sum games with bilinear loss functions. We prove structural results that can be used to find certain Nash-equilibria with a single separable convex minimization.
by Swati Gupta.
Ph. D.
Collins, Jarred T. "Moore - Greig designs - a new combinatorial structure /." View online ; access limited to URI, 2005. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3186900.
Повний текст джерелаLi, Quan Ph D. Massachusetts Institute of Technology. "Algorithms and algorithmic obstacles for probabilistic combinatorial structures." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115765.
Повний текст джерелаCataloged from PDF version of thesis.
Includes bibliographical references (pages 209-214).
We study efficient 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 optimization for three NP-hard combinatorial optimization problems: Large Submatrix Selection, Maximum Cut (Max-Cut) of a graph and Matrix Completion. The Large Submatrix Selection problem is to find a k x k submatrix of an n x n matrix with i.i.d. standard Gaussian entries, which has the largest average entry. It was shown in [13] using non-constructive methods that the largest average value of a k x k submatrix is 2(1 + o(1) [square root] log n/k with high probability (w.h.p.) when k = O(log n/ log log n). We show that a natural greedy algorithm called Largest Average Submatrix LAS produces a submatrix with average value (1+ o(1)) [square root] 2 log n/k w.h.p. when k is constant and n grows, namely approximately [square root] 2 smaller. Then by drawing an analogy with the problem of finding cliques in random graphs, we propose a simple greedy algorithm which produces a k x k matrix with asymptotically the same average value (1+o(1) [square root] 2log n/k w.h.p., for k = o(log n). Since the maximum clique problem is a special case of the largest submatrix problem and the greedy algorithm is the best known algorithm for finding cliques in random graphs, it is tempting to believe that beating the factor [square root] 2 performance gap suffered by both algorithms might be very challenging. Surprisingly, we show the existence of a very simple algorithm which produces a k x k matrix with average value (1 + o[subscript]k(1) + o(1))(4/3) [square root] 2log n/k for k = o((log n)¹.⁵), that is, with asymptotic factor 4/3 when k grows. To get an insight into the algorithmic hardness of this problem, and motivated by methods originating in the theory of spin glasses, we conduct the so-called expected overlap analysis of matrices with average value asymptotically (1 + o(1))[alpha][square root] 2 log n/k for a fixed value [alpha] [epsilon] [1, fixed value a E [1, [square root]2]. The overlap corresponds to the number of common rows and common columns for pairs of matrices achieving this value. We discover numerically an intriguing phase transition at [alpha]* [delta]= 5[square root]2/(3[square root]3) ~~ 1.3608.. [epsilon] [4/3, [square root]2]: when [alpha] < [alpha]* the space of overlaps is a continuous subset of [0, 1]², whereas [alpha] = [alpha]* marks the onset of discontinuity, and as a result the model exhibits the Overlap Gap Property (OGP) when [alpha] > [alpha]*, appropriately defined. We conjecture that OGP observed for [alpha] > [alpha]* also marks the onset of the algorithmic hardness - no polynomial time algorithm exists for finding matrices with average value at least (1+o(1)[alpha][square root]2log n/k, when [alpha] > [alpha]* and k is a growing function of n. Finding a maximum cut of a graph is a well-known canonical NP-hard problem. We consider the problem of estimating the size of a maximum cut in a random Erdős-Rényi graph on n nodes and [cn] edges. We establish that the size of the maximum cut normalized by the number of nodes belongs to the interval [c/2 + 0.47523[square root]c,c/2 + 0.55909[square root]c] w.h.p. as n increases, for all sufficiently large c. We observe that every maximum size cut satisfies a certain local optimality property, and we compute the expected number of cuts with a given value satisfying this local optimality property. Estimating this expectation amounts to solving a rather involved multi-dimensional large deviations problem. We solve this underlying large deviation problem asymptotically as c increases and use it to obtain an improved upper bound on the Max-Cut value. The lower bound is obtained by application of the second moment method, coupled with the same local optimality constraint, and is shown to work up to the stated lower bound value c/2 + 0.47523[square root]c. We also obtain an improved lower bound of 1.36000n on the Max-Cut for the random cubic graph or any cubic graph with large girth, improving the previous best bound of 1.33773n. Matrix Completion is the problem of reconstructing a rank-k n x n matrix M from a sampling of its entries. We propose a new matrix completion algorithm using a novel sampling scheme based on a union of independent sparse random regular bipartite graphs. We show that under a certain incoherence assumption on M and for the case when both the rank and the condition number of M are bounded, w.h.p. our algorithm recovers an [epsilon]-approximation of M in terms of the Frobenius norm using O(nlog² (1/[epsilon])) samples and in linear time O(nlog² (1/[epsilon])). This provides the best known bounds both on the sample complexity and computational cost for reconstructing (approximately) an unknown low-rank matrix. The novelty of our algorithm is two new steps of thresholding singular values and rescaling singular vectors in the application of the "vanilla" alternating minimization algorithm. The structure of sparse random regular graphs is used heavily for controlling the impact of these regularization steps.
by Quan Li.
Ph. D.
Sinclair, Alistair John. "Randomised algorithms for counting and generating combinatorial structures." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/11392.
Повний текст джерелаSobkowiak, Jessica. "Some combinatorial structures constructed from modular Leonard triples." [Tampa, Fla] : University of South Florida, 2009. http://purl.fcla.edu/usf/dc/et/SFE0002978.
Повний текст джерелаÓMáille, Paul E. "Combinatorial protein engineering by structure-based gene shuffling /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486572165277805.
Повний текст джерелаGay, Joël. "Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS209/document.
Повний текст джерелаAlgebraic combinatorics is the research field that uses combinatorial methods and algorithms to study algebraic computation, and applies algebraic tools to combinatorial problems. One of the central topics of algebraic combinatorics is the study of permutations, interpreted in many different ways (as bijections, permutation matrices, words over integers, total orders on integers, vertices of the permutahedron…). This rich diversity of perspectives leads to the following generalizations of the symmetric group. On the geometric side, the symmetric group generated by simple transpositions is the canonical example of finite reflection groups, also called Coxeter groups. On the monoidal side, the simple transpositions become bubble sort operators that generate the 0-Hecke monoid, whose algebra is the specialization at q=0 of Iwahori’s q-deformation of the symmetric group. This thesis deals with two further generalizations of permutations. In the first part of this thesis, we first focus on partial permutations matrices, that is placements of pairwise non attacking rooks on a n by n chessboard, simply called rooks. Rooks generate the rook monoid, a generalization of the symmetric group. In this thesis we introduce and study the 0-Rook monoid, a generalization of the 0-Hecke monoid. Its algebra is a proper degeneracy at q = 0 of the q-deformed rook monoid of Solomon. We study fundamental monoidal properties of the 0-rook monoid (Green orders, lattice property of the R-order, J-triviality) which allow us to describe its representation theory (simple and projective modules, projectivity on the 0-Hecke monoid, restriction and induction along an inclusion map).Rook monoids are actually type A instances of the family of Renner monoids, which are completions of the Weyl groups (crystallographic Coxeter groups) for Zariski’s topology. In the second part of this thesis we extend our type A results to define and give a presentation of 0-Renner monoids in type B and D. This also leads to a presentation of the Renner monoids of type B and D, correcting a misleading presentation that appeared earlier in the litterature. As in type A we study the monoidal properties of the 0-Renner monoids of type B and D : they are still J-trivial but their R-order are not lattices anymore. We study nonetheless their representation theory and the restriction of projective modules over the corresponding 0-Hecke monoids. The third part of this thesis deals with different generalizations of permutations. In a recent series of papers, Châtel, Pilaud and Pons revisit the algebraic combinatorics of permutations (weak order, Malvenuto-Reutenauer Hopf algebra) in terms of the combinatorics of integer posets. This perspective encompasses as well the combinatorics of quotients of the weak order such as binary trees, binary sequences, and more generally the recent permutrees of Pilaud and Pons. We generalize the weak order on the elements of the Weyl groups. This enables us to describe the order on vertices of the permutahedra, generalized associahedra and cubes in the same unified context. These results are based on subtle properties of sums of roots in Weyl groups, and actually fail for non-crystallographic Coxeter groups
Perarnau, Llobet Guillem. "Random combinatorial structures with low dependencies : existence and enumeration." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/362940.
Повний текст джерелаIn this thesis we study different problems in combinatorics and in graph theory by means of the probabilistic method. This method, introduced by Erdös, has become an extremely powerful tool to provide existential proofs for certain problems in different mathematical branches where other methods had failed utterly. One of its main concerns is to study the behavior of random variables. In particular, one common situation arises when these random variables count the number of bad events that occur in a combinatorial structure. The idea of the Poisson Paradigm is to estimate the probability of these bad events not happening at the same time when the dependencies among them are weak or rare. If this is the case, this probability should behave similarly as in the case where all the events are mutually independent. This idea gets reflected in several well-known tools, such as the Lovász Local Lemma or Suen inequality. The goal of this thesis is to study these techniques by setting new versions or refining the existing ones for particular cases, as well as providing new applications of them for different problems in combinatorics and graph theory. Next, we enumerate the main contributions of this thesis. The first part of this thesis extends a result of Erdös and Spencer on latin transversals [1]. They showed that an integer matrix such that no number appears many times, admits a latin transversal. This is equivalent to study rainbow matchings of edge-colored complete bipartite graphs. Under the same hypothesis of, we provide enumerating results on such rainbow matchings. The second part of the thesis deals with identifying codes, a set of vertices such that all vertices in the graph have distinct neighborhood within the code. We provide bounds on the size of a minimal identifying code in terms of the degree parameters and partially answer a question of Foucaud et al. On a different chapter of the thesis, we show that any dense enough graph has a very large spanning subgraph that admits a small identifying code. In some cases, proving the existence of a certain object is trivial. However, the same techniques allow us to obtain enumerative results. The study of permutation patterns is a good example of that. In the third part of the thesis we devise a new approach in order to estimate how many permutations of given length avoid a consecutive copy of a given pattern. In particular, we provide upper and lower bounds for them. One of the consequences derived from our approach is a proof of the CMP conjecture, stated by Elizalde and Noy as well as some new results on the behavior of most of the patterns. In the last part of this thesis, we focus on the Lonely Runner Conjecture, posed independently by Wills and Cusick and that has multiple applications in different mathematical fields. This well-known conjecture states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a moment where all of them are far enough from the origin. We improve the result of Chen on the gap of loneliness by studying the time when two runners are close to the origin. We also show an invisible runner type result, extending a result of Czerwinski and Grytczuk.
Asim, Muhammad Ahsan. "Network Testing in a Testbed Simulator using Combinatorial Structures." Thesis, Blekinge Tekniska Högskola, Avdelningen för för interaktion och systemdesign, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-6058.
Повний текст джерела14:36 Folkparksvagan Ronneby 372 40 Sweden
Henderson, Roger William. "Cryptanalysis of braid group cryptosystem and related combinatorial structures." Thesis, Royal Holloway, University of London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440519.
Повний текст джерелаJones, Sian K. "On the enumeration of sudoku and similar combinatorial structures." Thesis, University of South Wales, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.541662.
Повний текст джерелаConner, Andrew Brondos 1981. "A(infinity)-structures, generalized Koszul properties, and combinatorial topology." Thesis, University of Oregon, 2011. http://hdl.handle.net/1794/11559.
Повний текст джерелаMotivated by the Adams spectral sequence for computing stable homotopy groups, Priddy defined a class of algebras called Koszul algebras with nice homological properties. Many important algebras arising naturally in mathematics are Koszul, and the Koszul property is often tied to important structure in the settings which produced the algebras. However, the strong defining conditions for a Koszul algebra imply that such algebras must be quadratic. A very natural generalization of Koszul algebras called K 2 algebras was recently introduced by Cassidy and Shelton. Unlike other generalizations of the Koszul property, the class of K 2 algebras is closed under many standard operations in ring theory. The class of K 2 algebras includes Artin-Schelter regular algebras of global dimension 4 on three linear generators as well as graded complete intersections. Our work comprises two distinct projects. Each project was motivated by an aspect of the theory of Koszul algebras which we regard as sufficiently powerful or fundamental to warrant an interpretation for K 2 algebras. A very useful theorem due to Backelin and Fröberg states that if A is a Koszul algebra and I is a quadratic ideal of A which is Koszul as a left A -module, then the factor algebra A/I is a Koszul algebra. We prove that if A is Koszul algebra and A I is a K 2 module, then A/I is a K 2 algebra provided A/I acts trivially on Ext A ( A/I,k ). As an application of our theorem, we show that the class of sequentially Cohen-Macaulay Stanley-Reisner rings are K 2 algebras and we give examples that suggest the class of K 2 Stanley-Reisner rings is actually much larger. Another important recent development in ring theory is the use of A ∞ -algebras. One can characterize Koszul algebras as those graded algebras whose Yoneda algebra admits only trivial A ∞ -structure. We show that, in contrast to the situation for Koszul algebras, vanishing of higher A ∞ -structure on the Yoneda algebra of a K 2 algebra need not be determined in any obvious way by the degrees of defining relations. We also demonstrate that obvious patterns of vanishing among higher multiplications cannot detect the K 2 property. This dissertation includes previously unpublished co-authored material.
Committee in charge: Dr. Brad Shelton, Chair; Dr. Victor Ostrik, Member; Dr. Nicholas Proudfoot, Member; Dr. Arkady Vaintrob, Member; Dr. David Boush, Outside Member
Fournier, Bradford M. "Towards a Theory of Recursive Function Complexity: Sigma Matrices and Inverse Complexity Measures." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2072.
Повний текст джерелаRisley, Rebecca N. "A Generalization of Sturmian Sequences: Combinatorial Structure and Transcendence." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278440/.
Повний текст джерелаPhillips, Linzy. "Erasure-correcting codes derived from Sudoku & related combinatorial structures." Thesis, University of South Wales, 2013. https://pure.southwales.ac.uk/en/studentthesis/erasurecorrecting-codes-derived-from-sudoku--related-combinatorial-structures(b359130e-bfc2-4df0-a6f5-55879212010d).html.
Повний текст джерелаGhannadian, Farzad. "The structure of the solution space and its relation to execution time of evolutionary algorithms with applications." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15687.
Повний текст джерелаMatsuura, Akihiro. "Combinatorial Structures in Finite Automata, CNF Satisfiability and Arithmetic Computation." 京都大学 (Kyoto University), 2002. http://hdl.handle.net/2433/149387.
Повний текст джерелаSharma, Dushyant 1975. "Cyclic exchange and related neighborhood structures for combinatorial optimization problems." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8526.
Повний текст джерелаIncludes bibliographical references (p. 122-126).
In this thesis, we concentrate on neighborhood search algorithms based on very large-scale neighborhood structures. The thesis consists of three parts. In the first part, we develop a cyclic exchange neighborhood search based approach for partitioning problems. A partitioning problem is to divide a set of n elements into K subsets S1,... ,SK so as to minimize f(S1)+...+f(SK) for some specified function f. A partition S'1,.. ,S'K is called a cyclic exchange neighbor of the partition S1,...,SK if [...]. The problem of searching the cyclic exchange neighborhood is NP-hard. We develop new exact and heuristic algorithms to search this neighborhood structure. We propose cyclic exchange based neighborhood search algorithms for specific partitioning problems. We provide computational results on these problems indicating that the cyclic exchange is very effective and can be implemented efficiently in practice. The second part deals with the Combined Through and Fleet Assignment Model (ctFAM). This model integrates two airline planning models: (i) Fleet Assignment Model and (ii) Through Assignment Model, which are currently solved in a sequential manner because the combined problem is too large. This leads to sub-optimal solutions for the combined problem we develop very large-scale neighborhood search algorithms for the ctFAM. We also extend our neighborhood search algorithms to solve the multi-criteria objective function version of the ctFAM. Our computational results using real-life data show that neighborhood search can be a useful supplement to the current integer-programming optimization methods in airline scheduling.
(cont.) In the third part, we investigate the structure of neighborhoods in general. We call two neighborhood structures LO-equivalent if they have the same set of local optima for all instances of a combinatorial optimization problem. We define the extended neighborhood of a neighborhood structure N as the largest neighborhood structure that is LO-equivalent to N. In this thesis, we develop some theoretical properties of the extended neighborhood and relate these properties to the performance of a neighborhood structure. In particular, we show that the well-known 2-opt neighborhood structure for the Traveling Salesman Problem has a very large extended neighborhood, providing justification for its favorable empirical performance.
by Dushyant Sharma.
Ph.D.