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

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

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

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

As genome-sequencing costs continue their downward spiral, sequencing of closely related organisms has become increasingly a?ordable. The growing amount of genomic data available demands for the constant development of computational tools to be applied in comparative genomics. The RECOMB Workshop on C- parative Genomics (RECOMB-CG) is devoted to bringing together scientists working on all aspects of comparative genomics, from computer scientists, ma- ematicians and statisticians working on novel computational approaches for genome analysis and comparison, to biologists applying these computational tools to study the structure and the evolution of prokaryotic and eukaryotic genomes. This volume contains the 19 papers presented at the 7th Annual RECOMB-CG workshop held during September 27–29, 2009 at the Renyi Institute, in Budapest, Hungary. The papers published in these proceedings were selected for oral p- sentation from 31 submissions from scientists around the world. Each paper was reviewed by at least three members of the Program Committee in a stringent and thoughtful peer-review process.

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

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

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

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

As genome-sequencing costs continue their downward spiral, sequencing of closely related organisms has become increasingly a?ordable. The growing amount of genomic data available demands for the constant development of computational tools to be applied in comparative genomics. The RECOMB Workshop on C- parative Genomics (RECOMB-CG) is devoted to bringing together scientists working on all aspects of comparative genomics, from computer scientists, ma- ematicians and statisticians working on novel computational approaches for genome analysis and comparison, to biologists applying these computational tools to study the structure and the evolution of prokaryotic and eukaryotic genomes. This volume contains the 19 papers presented at the 7th Annual RECOMB-CG workshop held during September 27–29, 2009 at the Renyi Institute, in Budapest, Hungary. The papers published in these proceedings were selected for oral p- sentation from 31 submissions from scientists around the world. Each paper was reviewed by at least three members of the Program Committee in a stringent and thoughtful peer-review process.