Download or read book Perfect Matchings written by Cláudio L. Lucchesi and published by Springer Nature. This book was released on 2024 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matching Theory written by László Lovász and published by American Mathematical Soc.. This book was released on 2009 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. Besides basic results on the existence of matchings and on the matching structure of graphs, the impact of matching theory is discussed by providing crucial special cases and nontrivial examples on matroid theory, algorithms, and polyhedral combinatorics. The new Appendix outlines how the theory and applications of matching theory have continued to develop since the book was first published in 1986, by launching (among other things) the Markov Chain Monte Carlo method.
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2016-08-16 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.
Download or read book Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems written by Roman Barták and published by Springer. This book was released on 2005-05-24 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR2005)washeldinPrague,CzechRepublic,duringMay31–June1,2005. The conference is intended primarily as a forum to focus on the integration and hybridization of the approaches of constraint programming (CP), arti?cial intelligence (AI), and operations research (OR) technologies for solving large-scale and complex real-life optimization problems. Therefore, CPAIOR is never far from industrial applications. The high number of submissions received this year, almost 100 papers, in witness to the interest of the research community in this conference. From these submissions, we chose 26 to be published in full in the proceedings. This volume includes summaries of the invited talks of CPAIOR: one from industry, one from the embedded system research community, and one from the operations research community. The invited speakers were: Filippo Focacci from ILOGS.A.,France,oneoftheleadingcompaniesinthe?eld;PaulPop,professor in the Embedded Systems Lab in the Computer and Information Science - partment, Link ̈ oping University; and Paul Williams, full professor of Operations Research at the London School of Economics. The day before CPAIOR, a Master Class was organized by Gilles Pesant, where leading researchers gave introductory and overview talks in the area of metaheuristics and constraint programming. The Master Class was intended for PhD students, researchers, and practitioners. We are very grateful to Gilles who brought this excellent program together. For conference publicity we warmly thank Willem Jan van Hoeve and Petr Vil ́ ?m who did a great job with the high number of submissions received.
Download or read book Combinatorial Optimization written by Alexander Schrijver and published by Springer Science & Business Media. This book was released on 2003-02-12 with total page 2024 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as "the Lawler" simply. I think that now, with this volume Springer has landed a coup: "The Schrijver". The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency." OR-Spectrum
Download or read book Computing and Combinatorics written by Chi-Yeh Chen and published by Springer Nature. This book was released on 2021-10-21 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 27th International Conference on Computing and Combinatorics, COCOON 2021, held in Tainan, Taiwan, in October 2021. Due to the COVID-19 pandemic, COCOON 2021 was organized as a hybrid conference. The 56 papers presented in this volume were carefully reviewed and selected from 131 submissions. The papers are divided into the following topical sub-headings: algorithms, approximation algorithms, automata, computational geometry, fault tolerant computing and fault diagnosis, graph algorithms, graph theory and applications, network and algorithms, online algorithm and stream algorithms, parameterized complexity and algorithms, and recreational games.
Download or read book Dualities in graphs and digraphs written by Hatzel, Meike and published by Universitätsverlag der TU Berlin. This book was released on 2023-05-23 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we describe dualities in directed as well as undirected graphs based on tools such as width-parameters, obstructions and substructures. We mainly focus on directed graphs and their structure. In the context of a long open conjecture that bounds the monotonicity costs of a version of the directed cops and robber game, we introduce new width-measures based on directed separations that are closely related to DAG-width. We identify a tangle-like obstruction for which we prove a duality theorem. Johnson, Reed, Robertson, Seymour and Thomas introduced the width measure directed treewidth as a generalisation of treewidth for directed graphs. We introduce a new width measure, the cyclewidth, which is parametrically equivalent to directed treewidth. Making use of the connection between directed graphs and bipartite graphs with perfect matchings we characterise the digraphs of low cyclewidth. Generalising the seminal work by Robertson and Seymour resulting in a global structure theorem for undirected graphs, there is the goal of obtaining a structure theorem, based on directed treewidth, describing the structure of the directed graphs excluding a fixed butterfly minor. Working in this direction we present a new flat wall theorem for directed graphs which we believe to provide a better base for a directed structure theorem than the existing ones. On undirected graphs we present several results on induced subgraphs in the graphs themselves or the square graph of their linegraph. These results range from general statements about all graphs to the consideration of specific graph classes such as the one with exactly two moplexes. In der vorliegenden Arbeit beschreiben wir Dualitäten in gerichteten sowie in ungerichteten Graphen basierend auf Konzepten wie Weiteparametern, Obstruktionen und Substrukturen. Der Hauptfokus der Arbeit liegt bei gerichteten Graphen und ihrer Struktur. Im Kontext einer lange offenen Vermutung, dass die Monotoniekosten einer Variante des Räuber und Gendarm Spiels für gerichtete Graphen beschränkt sind, führen wir neue Weiteparameter ein, die auf gerichteten Separationen basieren und eng mit DAG-Weite verwandt sind. Wir identifizieren Tangle-artige Obstruktionen zu diesen Weiteparametern und beweisen die Dualität zwischen diesen beiden Konzepten. Johnson, Reed, Robertson, Seymour und Thomas haben die gerichtete Baumweite als gerichtete Verallgemeinerung der Baumweite auf ungerichteten Graphen eingeführt. Wir führen einen neuen Weiteparameter, die Cyclewidth, ein, der parametrisch equivalent zur gerichteten Baumweite ist. Unter Nutzung der Verwandtschaft von gerichteten Graphen und bipartiten Graphen mit perfekten Matchings charakterisieren wir die gerichteten Graphen mit kleiner Cyclewidth. Ein einschlagendes Ergebnis in der Graphenstrukturtheorie ist das Strukturtheorem von Robertson und Seymour. Basierend darauf gibt es Anstrengungen ein solches Strukturtheorem auch für gerichtete Graphen zu finden und dafür die gerichtete Baumweite als Grundlage zu nutzen. Dieses Theorem soll die Struktur aller gerichteten Graphen beschreiben, die einen festen gerichteten Graphen als Butterflyminoren ausschließen. In diesem Kontext beweisen wir ein neues Flat-wall-theorem für gerichtete Graphen, dass unserer Erwartung nach eine bessere Basis für ein gerichtetes Strukturtheorem bietet als die bisher betrachteten Alternativen. Auf ungerichteten Graphen präsentieren wir einige Ergebnisse bezüglich induzierten Subgraphen in gegebenen Graphen oder ihren Linegraphen. Diese Ergebnisse reichen von der Betrachtung spezifischer Graphklassen, wie den Graphen mit zwei Moplexen, bis zu Ergebnissen auf der allgemeinen Klasse aller Graphen.
Download or read book Computational Complexity of Counting and Sampling written by Istvan Miklos and published by CRC Press. This book was released on 2019-02-21 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared toward researchers in enumerative combinatorics, discrete mathematics, and theoretical computer science. The book covers the following topics: Counting and sampling problems that are solvable in polynomial running time, including holographic algorithms; #P-complete counting problems; and approximation algorithms for counting and sampling. First, it opens with the basics, such as the theoretical computer science background and dynamic programming algorithms. Later, the book expands its scope to focus on advanced topics, like stochastic approximations of counting discrete mathematical objects and holographic algorithms. After finishing the book, readers will agree that the subject is well covered, as the book starts with the basics and gradually explores the more complex aspects of the topic. Features: Each chapter includes exercises and solutions Ideally written for researchers and scientists Covers all aspects of the topic, beginning with a solid introduction, before shifting to computational complexity’s more advanced features, with a focus on counting and sampling
Download or read book Matching minors in bipartite graphs written by Wiederrecht, Sebastian and published by Universitätsverlag der TU Berlin. This book was released on 2022-04-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs. We develope matching theoretic to established results of graph minor theory: We characterise the existence of a cross over a conformal cycle by means of a topological property. Furthermore, we develope a theory for perfect matching width, a width parameter for graphs with perfect matchings introduced by Norin. here we show that the disjoint alternating paths problem can be solved in polynomial time on graphs of bounded width. Moreover, we show that every bipartite graph with high perfect matching width must contain a large grid as a matching minor. Finally, we prove an analogue of the we known Flat Wall theorem and provide a qualitative description of all bipartite graphs which exclude a fixed matching minor. In der vorliegenden Arbeit werden fundamentale Teile des Graphminorenprojekts von Robertson und Seymour für das Studium von Matching Minoren adaptiert und Verbindungen zur Strukturtheorie gerichteter Graphen aufgezeigt. Wir entwickeln matchingtheoretische Analogien zu etablierten Resultaten des Graphminorenprojekts: Wir charakterisieren die Existenz eines Kreuzes über einem konformen Kreis mittels topologischer Eigenschaften. Weiter entwickeln wir eine Theorie zu perfekter Matchingweite, einem Weiteparameter für Graphen mit perfekten Matchings, der von Norin eingeführt wurde. Hier zeigen wir, dass das Disjunkte Alternierende Pfade Problem auf bipartiten Graphen mit beschränkter Weite in Polynomialzeit lösbar ist. Weiter zeigen wir, dass jeder bipartite Graph mit hoher perfekter Matchingweite ein großes Gitter als Matchingminor enthalten muss. Schließlich zeigen wir ein Analogon des bekannten Flat Wall Theorem und geben eine qualitative Beschreibung aller bipartiter Graphen an, die einen festen Matching Minor ausschließen.
Download or read book Handbook of Graph Theory Combinatorial Optimization and Algorithms written by Krishnaiyan "KT" Thulasiraman and published by CRC Press. This book was released on 2016-01-05 with total page 1217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c
Download or read book Graph Polynomials written by Yongtang Shi and published by CRC Press. This book was released on 2016-11-25 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.
Download or read book Erdos Ko Rado Theorems Algebraic Approaches written by Christopher Godsil and published by Cambridge University Press. This book was released on 2016 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.
Download or read book Bipartite Graphs and Their Applications written by Armen S. Asratian and published by Cambridge University Press. This book was released on 1998-07-13 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, Chemistry, Communication Networks and Computer Science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.
Download or read book Integer Programming and Related Areas written by Rabe v. Randow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of integer programming and combinatorial optimization continue to be areas of great vitality, with an ever increasing number of publications and journals appearing. A classified bibliography thus continues to be necessary and useful today, even more so than it did when the project, of which this is the fifth volume, was started in 1970 in the Institut fur Okonometrie und Operations Research of the University of Bonn. The pioneering first volume was compiled by Claus Kastning during the years 1970 - 1975 and appeared in 1976 as Volume 128 of the series Lecture Notes in Economics and Mathematical Systems published by the Springer Verlag. Work on the project was continued by Dirk Hausmann, Reinhardt Euler, and Rabe von Randow, and resulted in the publication of the second, third, and fourth volumes in 1978, 1982, and 1985 (Volumes 160, 197, and 243 of the above series). The present book constitutes the fifth volume of the bibliography and covers the period from autumn 1984 to the end of 1987. It contains 5864 new publications by 4480 authors and was compiled by Rabe von Randow. Its form is practically identical to that of the first four volumes, some additions having been made to the subject list.
Download or read book Graph Drawing and Network Visualization written by Michael A. Bekos and published by Springer Nature. This book was released on 2024-01-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set LNCS 14465-14466 constitutes the proceedings of the 31st International Symposium on Graph Drawing and Network Visualization, GD 2023, held in Isola delle Femmine, Palermo, Italy, in September 2023. The 31 full papers, 7 short papers, presented together with 2 invited talks, and one contest report, were thoroughly reviewed and selected from the 100 submissions. The abstracts of 11 posters presented at the conference can be found in the back matter of the volume. The contributions were organized in topical sections as follows: beyond planarity; crossing numbers; linear layouts; geometric aspects; visualization challenges; graph representations; graph decompositions; topological aspects; parameterized complexity for drawings; planar graphs; frameworks; algorithmics.
Download or read book The Nature of Computation written by Cristopher Moore and published by OUP Oxford. This book was released on 2011-08-12 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.
Download or read book Randomized Algorithms written by Rajeev Motwani and published by Cambridge University Press. This book was released on 1995-08-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.
