Open AccessBook
Kernelization: Theory of Parameterized Preprocessing
Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Meirav Zehavi +3 more
- 28 Feb 2019
246
TL;DR: Kernelization: Theory of Parameterized Preprocessing, by Fomin et al., is unique in that it is a text focusing solely on the titular topic of kernelization, and is able to more effectively showcase and teach the tools used in the field than a more traditional text on fixed parameter complexity.
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Abstract: 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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Citations
•Posted Content
Bidimensionality and Kernels
TL;DR: It is shown that "essentially" all bidimensional problems not only have sub-exponential time algorithms and PTASs but they also have linear kernels, affirmatively answering an open question from ACM 2005, where the existence of linear kernels was conjectured for the first time.
80
•Journal Article
A Parameterized View on Matroid Optimization Problems
TL;DR: If the ground set of a represented matroid is partitioned into blocks of size l, then it can be determined in f(k, (l) n 0(1) randomized time whether there is an independent set that is the union of k blocks.
72
A survey of parameterized algorithms and the complexity of edge modification
TL;DR: A comprehensive overview of parameterized algorithms for graph modification problems is given in this article , where the main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties.
27
Parameterized Low-Rank Binary Matrix Approximation
TL;DR: This work starts the systematic algorithmic study of low-rank binary matrix approximation from the perspective of parameterized complexity and shows in which cases and under what conditions the problem is fixed-parameter tractable, admits a polynomial kernel and can be solved in parameterized subexponential time.
•Posted Content
Finding cuts of bounded degree: complexity, FPT and exact algorithms, and kernelization
TL;DR: In this paper, a generalization of the matching cut problem, called $d$-cut, is introduced, which is a bipartition of the vertex set of a graph into two sets of vertices such that each vertex has at most one neighbor in the other side of the cut.
References
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Thomas H. Cormen,Charles E. Leiserson,Ronald L. Rivest +2 more
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TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
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Approximation Algorithms
Vijay V. Vazirani
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TL;DR: Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field.
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Alexander Schrijver
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TL;DR: This book shows the combinatorial optimization polyhedra and efficiency as your friend in spending the time in reading a book.
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Computational Complexity: A Modern Approach
Sanjeev Arora,Boaz Barak +1 more
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TL;DR: This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory and can be used as a reference for self-study for anyone interested in complexity.
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Graph Theory
J. A. Bondy,U.S.R Murty +1 more
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TL;DR: This book provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal, and is suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science.
3.6K