Martin Dietzfelbinger

A self-contained treatment of theoretically and practically important efficient algorithms for the primality problem. The text covers the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal and Saxena. The volume is written for students of computer science, in particular those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.

From Randomized Algorithms to "PRIMES Is in P"

Primality Testing in Polynomial Time

Zoltán Ésik

Ersébet Csuhaj-Varjú

This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.

39th International Symposium, MFCS 2014, Budapest, Hungary, August 26-29, 2014. Proceedings, Part I

Mathematical Foundations of Computer Science 2014

Peter Sanders

Kurt Mehlhorn

Algorithmen bilden das Herzstück jeder nichttrivialen Anwendung von Computern, und die Algorithmik ist ein modernes und aktives Gebiet der Informatik. Daher sollte sich jede Informatikerin und jeder Informatiker mit den algorithmischen Grundwerkzeugen auskennen. Dies sind Strukturen zur effizienten Organisation von Daten, häufig benutzte Algorithmen und Standardtechniken für das Modellieren, Verstehen und Lösen algorithmischer Probleme. Dieses Buch ist eine straff gehaltene Einführung in die Welt dieser Grundwerkzeuge, gerichtet an Studierende und im Beruf stehende Experten, die mit dem Programmieren und mit den Grundelementen der Sprache der Mathematik vertraut sind. Die einzelnen Kapitel behandeln Arrays und verkettete Listen, Hashtabellen und assoziative Arrays, Sortieren und Auswählen, Prioritätswarteschlangen, sortierte Folgen, Darstellung von Graphen, Graphdurchläufe, kürzeste Wege, minimale Spannbäume und Optimierung. Die Algorithmen werden auf moderne Weise präsentiert, mit explizit angegebenen Invarianten, und mit Kommentaren zu neueren Entwicklungen wie Algorithm Engineering, Speicherhierarchien, Algorithmenbibliotheken und zertifizierenden Algorithmen. Die Algorithmen werden zunächst mit Hilfe von Bildern, Text und Pseudocode erläutert; dann werden Details zu effizienten Implementierungen gegeben, auch in Bezug auf konkrete Sprachen wie C++ und Java.

Die Grundwerkzeuge

Algorithmen und Datenstrukturen

Roman Dementiev

This textbook is a concise introduction to the basic toolbox of structures that allow efficient organization and retrieval of data, key algorithms for problems on graphs, and generic techniques for modeling, understanding, and solving algorithmic problems. The authors aim for a balance between simplicity and efficiency, between theory and practice, and between classical results and the forefront of research. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, optimization, collective communication and computation, and load balancing. The authors also discuss important issues such as algorithm engineering, memory hierarchies, algorithm libraries, and certifying algorithms. Moving beyond the sequential algorithms and data structures of the earlier related title, this book takes into account the paradigm shift towards the parallel processing required to solve modern performance-critical applications and how this impacts on the teaching of algorithms. The book is suitable for undergraduate and graduate students and professionals familiar with programming and basic mathematical language. Most chapters have the same basic structure: the authors discuss a problem as it occurs in a real-life situation, they illustrate the most important applications, and then they introduce simple solutions as informally as possible and as formally as necessary so the reader really understands the issues at hand. As they move to more advanced and optional issues, their approach gradually leads to a more mathematical treatment, including theorems and proofs. The book includes many examples, pictures, informal explanations, and exercises, and the implementation notes introduce clean, efficient implementations in languages such as C++ and Java.

The Basic Toolbox

Sequential and Parallel Algorithms and Data Structures

Berthold Vöcking

Helmut Alt

Rüdiger Reischuk

Christian Scheideler

Heribert Vollmer

Dorothea Wagner

Hinter vielen Computer-Programmen stecken intelligente Verfahren, die man als Algorithmen bezeichnet. Algorithmen lösen nicht nur mathematische Zahlen-Aufgaben, sondern auch ganz alltägliche Probleme: Wie ermittle ich den kürzesten Weg zwischen zwei Orten? Oder, wie kann ich einen Kuchen gerecht aufteilen? In diesem Buch erklären Informatiker 43 besonders elegante Algorithmen und illustrieren die Grundprinzipien des Algorithmendesigns anhand von interessanten Anwendungen, ohne dabei vom Leser spezielle Vorkenntnisse zu erwarten.

Taschenbuch der Algorithmen

39th International Symposium, MFCS 2014, Budapest, Hungary, August 26-29, 2014. Proceedings, Part II

Algorithms specify the way computers process information and how they execute tasks. Many recent technological innovations and achievements rely on algorithmic ideas – they facilitate new applications in science, medicine, production, logistics, traffic, communi¬cation and entertainment. Efficient algorithms not only enable your personal computer to execute the newest generation of games with features unimaginable only a few years ago, they are also key to several recent scientific breakthroughs – for example, the sequencing of the human genome would not have been possible without the invention of new algorithmic ideas that speed up computations by several orders of magnitude. The greatest improvements in the area of algorithms rely on beautiful ideas for tackling computational tasks more efficiently. The problems solved are not restricted to arithmetic tasks in a narrow sense but often relate to exciting questions of nonmathematical flavor, such as: How can I find the exit out of a maze? How can I partition a treasure map so that the treasure can only be found if all parts of the map are recombined? How should I plan my trip to minimize cost? Solving these challenging problems requires logical reasoning, geometric and combinatorial imagination, and, last but not least, creativity – the skills needed for the design and analysis of algorithms. In this book we present some of the most beautiful algorithmic ideas in 41 articles written in colloquial, nontechnical language. Most of the articles arose out of an initiative among German-language universities to communicate the fascination of algorithms and computer science to high-school students. The book can be understood without any prior knowledge of algorithms and computing, and it will be an enlightening and fun read for students and interested adults.

Martin Dietzfelbinger

Books

Your next favorite book is out there