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Let S Start 2

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Let S Start 2

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Author : Воронка Зірка
language : en
Publisher: Geneza
Release Date : 1994-01-01

Let S Start 2 written by Воронка Зірка and has been published by Geneza this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Foreign Language Study categories.

Навчально-методичний комплекс "Let's start!-2" розраховано на дітей, що вивчають англійську мову другий рік.

Let S Start 2

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Author : Воронка Зірка
language : en
Publisher: Geneza
Release Date : 1994-01-01

Навчально-методичний комплекс "Let's Start! - 2" розрахований на дітей, що вивчають англійську мову другий рік.

Let S Start 2

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Author : Воронка Зірка
language : en
Publisher: Geneza
Release Date : 1994-01-01

Книга для вчителя до частини 2.

Elements Of Dynamic And 2 Sat Programming Paths Trees And Cuts

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Author : Bentert, Matthias
language : en
Publisher: Universitätsverlag der TU Berlin
Release Date : 2021-11-18

Elements Of Dynamic And 2 Sat Programming Paths Trees And Cuts written by Bentert, Matthias and has been published by Universitätsverlag der TU Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Computers categories.

In dieser Arbeit entwickeln wir schnellere exakte Algorithmen (schneller bezüglich der Worst-Case-Laufzeit) für Spezialfälle von Graphproblemen. Diese Algorithmen beruhen größtenteils auf dynamischem Programmieren und auf 2-SAT-Programmierung. Dynamisches Programmieren beschreibt den Vorgang, ein Problem rekursiv in Unterprobleme zu zerteilen, sodass diese Unterprobleme gemeinsame Unterunterprobleme haben. Wenn diese Unterprobleme optimal gelöst wurden, dann kombiniert das dynamische Programm diese Lösungen zu einer optimalen Lösung des Ursprungsproblems. 2-SAT-Programmierung bezeichnet den Prozess, ein Problem durch eine Menge von 2-SAT-Formeln (aussagenlogische Formeln in konjunktiver Normalform, wobei jede Klausel aus maximal zwei Literalen besteht) auszudrücken. Dabei müssen erfüllende Wahrheitswertbelegungen für eine Teilmenge der 2-SAT-Formeln zu einer Lösung des Ursprungsproblems korrespondieren. Wenn eine 2-SAT-Formel erfüllbar ist, dann kann eine erfüllende Wahrheitswertbelegung in Linearzeit in der Länge der Formel berechnet werden. Wenn entsprechende 2-SAT-Formeln also in polynomieller Zeit in der Eingabegröße des Ursprungsproblems erstellt werden können, dann kann das Ursprungsproblem in polynomieller Zeit gelöst werden. Im folgenden beschreiben wir die Hauptresultate der Arbeit. Bei dem Diameter-Problem wird die größte Distanz zwischen zwei beliebigen Knoten in einem gegebenen ungerichteten Graphen gesucht. Das Ergebnis (der Durchmesser des Eingabegraphen) gehört zu den wichtigsten Parametern der Graphanalyse. In dieser Arbeit erzielen wir sowohl positive als auch negative Ergebnisse für Diameter. Wir konzentrieren uns dabei auf parametrisierte Algorithmen für Parameterkombinationen, die in vielen praktischen Anwendungen klein sind, und auf Parameter, die eine Distanz zur Trivialität messen. Bei dem Problem Length-Bounded Cut geht es darum, ob es eine Kantenmenge begrenzter Größe in einem Eingabegraphen gibt, sodass das Entfernen dieser Kanten die Distanz zwischen zwei gegebenen Knoten auf ein gegebenes Minimum erhöht. Wir bestätigen in dieser Arbeit eine Vermutung aus der wissenschaftlichen Literatur, dass Length-Bounded Cut in polynomieller Zeit in der Eingabegröße auf Einheitsintervallgraphen (Intervallgraphen, in denen jedes Intervall die gleiche Länge hat) gelöst werden kann. Der Algorithmus basiert auf dynamischem Programmieren. k-Disjoint Shortest Paths beschreibt das Problem, knotendisjunkte Pfade zwischen k gegebenen Knotenpaaren zu suchen, sodass jeder der k Pfade ein kürzester Pfad zwischen den jeweiligen Endknoten ist. Wir beschreiben ein dynamisches Programm mit einer Laufzeit n^O((k+1)!) für dieses Problem, wobei n die Anzahl der Knoten im Eingabegraphen ist. Dies zeigt, dass k-Disjoint Shortest Paths in polynomieller Zeit für jedes konstante k gelöst werden kann, was für über 20 Jahre ein ungelöstes Problem der algorithmischen Graphentheorie war. Das Problem Tree Containment fragt, ob ein gegebener phylogenetischer Baum T in einem gegebenen phylogenetischen Netzwerk N enthalten ist. Ein phylogenetisches Netzwerk (bzw. ein phylogenetischer Baum) ist ein gerichteter azyklischer Graph (bzw. ein gerichteter Baum) mit genau einer Quelle, in dem jeder Knoten höchstens eine ausgehende oder höchstens eine eingehende Kante hat und jedes Blatt eine Beschriftung trägt. Das Problem stammt aus der Bioinformatik aus dem Bereich der Suche nach dem Baums des Lebens (der Geschichte der Artenbildung). Wir führen eine neue Variante des Problems ein, die wir Soft Tree Containment nennen und die bestimmte Unsicherheitsfaktoren berücksichtigt. Wir zeigen mit Hilfe von 2-SAT-Programmierung, dass Soft Tree Containment in polynomieller Zeit gelöst werden kann, wenn N ein phylogenetischer Baum ist, in dem jeweils maximal zwei Blätter die gleiche Beschriftung tragen. Wir ergänzen dieses Ergebnis mit dem Beweis, dass Soft Tree Containment NP-schwer ist, selbst wenn N auf phylogenetische Bäume beschränkt ist, in denen jeweils maximal drei Blätter die gleiche Beschriftung tragen. Abschließend betrachten wir das Problem Reachable Object. Hierbei wird nach einer Sequenz von rationalen Tauschoperationen zwischen Agentinnen gesucht, sodass eine bestimmte Agentin ein bestimmtes Objekt erhält. Eine Tauschoperation ist rational, wenn beide an dem Tausch beteiligten Agentinnen ihr neues Objekt gegenüber dem jeweiligen alten Objekt bevorzugen. Reachable Object ist eine Verallgemeinerung des bekannten und viel untersuchten Problems Housing Market. Hierbei sind die Agentinnen in einem Graphen angeordnet und nur benachbarte Agentinnen können Objekte miteinander tauschen. Wir zeigen, dass Reachable Object NP-schwer ist, selbst wenn jede Agentin maximal drei Objekte gegenüber ihrem Startobjekt bevorzugt und dass Reachable Object polynomzeitlösbar ist, wenn jede Agentin maximal zwei Objekte gegenüber ihrem Startobjekt bevorzugt. Wir geben außerdem einen Polynomzeitalgorithmus für den Spezialfall an, in dem der Graph der Agentinnen ein Kreis ist. Dieser Polynomzeitalgorithmus basiert auf 2-SAT-Programmierung. This thesis presents faster (in terms of worst-case running times) exact algorithms for special cases of graph problems through dynamic programming and 2-SAT programming. Dynamic programming describes the procedure of breaking down a problem recursively into overlapping subproblems, that is, subproblems with common subsubproblems. Given optimal solutions to these subproblems, the dynamic program then combines them into an optimal solution for the original problem. 2-SAT programming refers to the procedure of reducing a problem to a set of 2-SAT formulas, that is, boolean formulas in conjunctive normal form in which each clause contains at most two literals. Computing whether such a formula is satisfiable (and computing a satisfying truth assignment, if one exists) takes linear time in the formula length. Hence, when satisfying truth assignments to some 2-SAT formulas correspond to a solution of the original problem and all formulas can be computed efficiently, that is, in polynomial time in the input size of the original problem, then the original problem can be solved in polynomial time. We next describe our main results. Diameter asks for the maximal distance between any two vertices in a given undirected graph. It is arguably among the most fundamental graph parameters. We provide both positive and negative parameterized results for distance-from-triviality-type parameters and parameter combinations that were observed to be small in real-world applications. In Length-Bounded Cut, we search for a bounded-size set of edges that intersects all paths between two given vertices of at most some given length. We confirm a conjecture from the literature by providing a polynomial-time algorithm for proper interval graphs which is based on dynamic programming. k-Disjoint Shortest Paths is the problem of finding (vertex-)disjoint paths between given vertex terminals such that each of these paths is a shortest path between the respective terminals. Its complexity for constant k > 2 has been an open problem for over 20 years. Using dynamic programming, we show that k-Disjoint Shortest Paths can be solved in polynomial time for each constant k. The problem Tree Containment asks whether a phylogenetic tree T is contained in a phylogenetic network N. A phylogenetic network (or tree) is a leaf-labeled single-source directed acyclic graph (or tree) in which each vertex has in-degree at most one or out-degree at most one. The problem stems from computational biology in the context of the tree of life (the history of speciation). We introduce a particular variant that resembles certain types of uncertainty in the input. We show that if each leaf label occurs at most twice in a phylogenetic tree N, then the problem can be solved in polynomial time and if labels can occur up to three times, then the problem becomes NP-hard. Lastly, Reachable Object is the problem of deciding whether there is a sequence of rational trades of objects among agents such that a given agent can obtain a certain object. A rational trade is a swap of objects between two agents where both agents profit from the swap, that is, they receive objects they prefer over the objects they trade away. This problem can be seen as a natural generalization of the well-known and well-studied Housing Market problem where the agents are arranged in a graph and only neighboring agents can trade objects. We prove a dichotomy result that states that the problem is polynomial-time solvable if each agent prefers at most two objects over its initially held object and it is NP-hard if each agent prefers at most three objects over its initially held object. We also provide a polynomial-time 2-SAT program for the case where the graph of agents is a cycle.

Integer Programming And Combinatorial Optimization

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Author : George Nemhauser
language : en
Publisher: Springer
Release Date : 2004-07-27

Integer Programming And Combinatorial Optimization written by George Nemhauser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-27 with Mathematics categories.

This volume contains the papers accepted for publication at IPCO X, the Tenth International Conference on Integer Programming and Combinatorial Optimization, held in New York City, New York, USA, June 7-11, 2004. The IPCO series of conferences presents recent results in theory, computation and applications of integer programming and combinatorial optimization. These conferences are sponsored by the Mathematical Programming Society, and are held in those years in which no International Symposium on Mathematical Programming takes place. IPCO VIII was held in Utrecht (The Netherlands) and IPCO IX was held in Cambridge (USA). A total of 109 abstracts, mostly of very high quality, were submitted. The Program Committee accepted 32, in order to meet the goal of having three days of talks with no parallel sessions. Thus, many excellent abstracts could not be accepted. The papers in this volume have not been refereed. It is expected that revised versions of the accepted papers will be submitted to standard scientific journals for publication. The Program Committee thanks all authors of submitted manuscripts for their support of IPCO. March 2004 George Nemhauser Daniel Bienstock Organization IPCO X was hosted by the Computational Optimization Research Center (CORC), Columbia University.

Graph Drawing And Network Visualization

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Author : Michael A. Bekos
language : en
Publisher: Springer Nature
Release Date : 2024-01-11

Graph Drawing And Network Visualization written by Michael A. Bekos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-11 with Computers categories.

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.

Data Mining For Association Rules And Sequential Patterns

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Author : Jean-Marc Adamo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Data Mining For Association Rules And Sequential Patterns written by Jean-Marc Adamo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

Recent advances in data collection, storage technologies, and computing power have made it possible for companies, government agencies and scientific laboratories to keep and manipulate vast amounts of data relating to their activities. This state-of-the-art monograph discusses essential algorithms for sophisticated data mining methods used with large-scale databases, focusing on two key topics: association rules and sequential pattern discovery. This will be an essential book for practitioners and professionals in computer science and computer engineering.

Boolean Constructions In Universal Algebras

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Author : A.G. Pinus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Boolean Constructions In Universal Algebras written by A.G. Pinus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics. This monograph is devoted to the fundamentals of the theory of Boolean constructions in universal algebra. Also considered are the problems of presenting different varieties of universal algebra with these constructions, and applications for investigating the spectra and skeletons of varieties of universal algebras. For researchers whose work involves universal algebra and logic.

Relation Algebras By Games

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Author : Robin Hirsch
language : en
Publisher: Elsevier
Release Date : 2002-08-15

Relation Algebras By Games written by Robin Hirsch and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-15 with Mathematics categories.

Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and games. After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises. The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise.

Non Additive Measures

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Author : Vicenc Torra
language : en
Publisher: Springer
Release Date : 2013-10-23

Non Additive Measures written by Vicenc Torra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Technology & Engineering categories.

This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field.

Let S Start 2

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