Fedor V. Fomin's Books

Kernelization

Theory of Parameterized Preprocessing

By: Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Meirav Zehavi

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Kernelization

Theory of Parameterized Preprocessing

By: Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Meirav Zehavi

Preprocessing, or data reduction, is a standard technique for simplifying and speeding up computation. Written by a team of experts in the field, this book introduces a rapidly developing area of preprocessing analysis known as kernelization. The authors provide an overview of basic methods and important results, with accessible explanations of the most recent advances in the area, such as meta-kernelization, representative sets, polynomial lower bounds, and lossy kernelization. The text is divided into four parts, which cover the different theoretical aspects of the area: upper bounds, meta-theorems, lower bounds, and beyond kernelization. The methods are demonstrated through extensive examples using a single data set. Written to be self-contained, the book only requires a basic background in algorithmics and will be of use to professionals, researchers and graduate students in theoretical computer science, optimization, combinatorics, and related fields.

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531

Publisher

Cambridge University Press

Published Date

ISBN 10

1108577334

ISBN 13

9781108577335

Exact Exponential Algorithms

By: Fedor V. Fomin,Dieter Kratsch

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Exact Exponential Algorithms

By: Fedor V. Fomin,Dieter Kratsch

For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.

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208

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642165338

ISBN 13

9783642165337

Parameterized Algorithms

By: Marek Cygan,Fedor V. Fomin,Łukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh

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Parameterized Algorithms

By: Marek Cygan,Fedor V. Fomin,Łukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

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Page Count

618

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Springer

Published Date

ISBN 10

3319212753

ISBN 13

9783319212753

Kernelization

Theory of Parameterized Preprocessing

By: Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Meirav Zehavi

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Kernelization

Theory of Parameterized Preprocessing

By: Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Meirav Zehavi

A complete introduction to recent advances in preprocessing analysis, or kernelization, with extensive examples using a single data set.

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531

Publisher

Cambridge University Press

Published Date

ISBN 10

1107057760

ISBN 13

9781107057760

Book's by Fedor V. Fomin

Kernelization

Kernelization

Exact Exponential Algorithms

Exact Exponential Algorithms

Parameterized Algorithms

Parameterized Algorithms

Kernelization

Kernelization

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