算法设计指南：方法、范式与复杂性分析

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"A guide-to-algorithm-design-paradigms-methods-and-complexity-analysis" 《算法设计指南：模式、方法与复杂性分析》是计算机科学领域的一本重要著作，由Anne Benoit、Yves Robert和Frédéric Vivien合著，属于Chapman & Hall/CRC的"应用算法与数据结构系列"。该书的高清英文版提供了最新版本的内容，旨在为专业人士提供算法设计和分析领域的前沿研究与应用。在计算机科学中，算法设计和数据结构的分析构成了学科的基础。随着现有算法和数据结构的改进以及新方法的引入，及时掌握最新的研究成果和应用变得至关重要。该系列书籍的目的是通过出版各种教科书、参考作品和手册，捕捉算法设计和分析领域的最新发展和应用。作者们强调，书中包含具体的实例和应用，使得理论知识更具实践意义。该系列涵盖的范围广泛，不仅限于以下几个领域： 1. 并行算法：研究如何在多处理器或分布式系统中同时执行任务，提高计算效率。 2. 近似算法：在无法找到最优解的情况下，寻找接近最优解的解决方案。 3. 随机化算法：利用随机元素来设计算法，提高性能或解决某些问题的可行性。 4. 图算法：处理图论中的问题，如最短路径、网络流等。 5. 搜索算法：包括排序、查找等，是计算机科学中最基本的算法之一。 6. 机器学习算法：用于让计算机从数据中学习规律，实现自动化预测和决策。 7. 医疗算法：应用于医疗领域的算法，例如疾病诊断、基因序列分析等。本书深入探讨了算法设计的不同范式和方法，同时关注算法的时间和空间复杂性分析，帮助读者理解算法效率，优化问题求解。无论是对初学者还是经验丰富的从业者，都能从中受益，提升其在算法设计与分析方面的专业能力。

Preface

Objective

YABA? Yet Another Book on Algorithms?

No thanks. There are so many good books on the design of algorithms that

it is hard to choose and pick one. If asked to name our two favorite refer-

ences, we would recommend Introduction to Algorithms by Cormen, Leiserson,

Rivest, and Stein [27] and Algorithms by Dasgupta, Papadimitriou, and Vazi-

rani [30]. For sure, this book does not intend to compete with such established

monuments.

Instead, this book proposes a complementary perspective. It aims at guid-

ing students and researchers who need to solve problems, either by ﬁnding

optimal algorithms or by assessing new complexity results. In a nutshell, the

main objective of this book is to outline the roadmap to follow, and to prac-

tice all the corresponding steps, in order to determine the complexity of a

problem.

Intended audience and use

The target audience for this book is graduate students and postgraduate re-

searchers in computer science and related ﬁelds.

This book does have prerequisites: We expect the reader to have some

experience with the design of algorithms, maybe through following an under-

graduate course in the ﬁeld, or through reading a few chapters of the reference

books quoted above. In particular, we assume that the reader is familiar with

classic algorithms, such as comparison-based sorting (e.g., quick sort or merge

sort), and has a good knowledge of elementary graph theory, including:

• traversals (depth-ﬁrst, breadth-ﬁrst, connected components);

• shortest paths (one-source, such as Dijkstra, all-pairs, such as Floyd–

Warshall);

• maximum matchings in bipartite graphs.

In fact, one needs to know only that eﬃcient algorithms exist to solve these

graph theory problems, but, of course, it is better to understand how they

work. Because excellent external sources already cover these topics, we refer

to them.

Also, we assume that readers have already been exposed, at least up to

some extent, to the basic paradigms of algorithm design: divide-and-conquer,

greedy algorithms, dynamic programming, and amortized analysis. But here,

rather than (or in addition to) referring to external sources, this book provides

xvi

extensive material so that the readers can assess their skills by solving the

many exercises in Part I.

Part II of this book can be used to teach an undergraduate or graduate class

on NP-completeness, with a focus on polynomial reductions, and a survey of

approaches that go beyond NP-completeness.

Part III of this book can be used to teach a graduate class on advanced

algorithms, either in the form of a series of classes presenting the case studies,

or in the form of projects assigned to students.

Book content and organization

The book is composed of three main parts:

• Part I: Polynomial-time algorithms: Exercises

• Part II: NP-completeness and beyond

• Part III: Reasoning on problem complexity

Part I aims at training the reader to design eﬃcient algorithms. To do

so, we provide a comprehensive set of problems to investigate. Problems are

organized along the main design principles, which we each revisit through a

brief introduction and a series of related exercises. This leads to ﬁve chapters:

1. Introduction to complexity

2. Divide-and-conquer

3. Greedy algorithms

4. Dynamic programming

5. Amortized analysis

All solutions to exercises are provided.

Part II deals with NP-completeness and beyond. Our coverage of NP-

completeness focuses on polynomial reductions. We deliberately ignore Tur-

ing machines and the theoretic arsenal. The (small) price to pay is to admit

Cook’s theorem, the existence of the canonical NP-complete problem, for-

mula satisﬁability, a.k.a. SAT. In Part II, we also cover approaches that go

beyond NP-completeness: identifying polynomial instances, approximation

algorithms, linear programming, randomized algorithms, branch-and-bound,

and backtracking. Part II consists of four chapters:

1. NP-completeness

2. Exercises on NP-completeness

3. Beyond NP-completeness

4. Exercises going beyond NP-completeness

All solutions to exercises are provided.

Part III constitutes the main originality of the book. It is devoted to case

studies whose goal is to provide the reader with tools and techniques to assess

problem complexity: which instances are polynomial, and which are NP-hard,

and what do to for the latter. Part III consists of an introduction summarizing

xvii

how to assess the complexity of a new problem, and it is illustrated with ﬁve

case studies:

1. Chains-on-chains partitioning

2. Replica placement in tree networks

3. Packet routing

4. Matrix product, or tiling the unit square

5. Online scheduling

Thanks

The content of this book, or at least preliminary versions of it, has been

used to teach courses at

Ecole Normale Sup´erieure de Lyon. We are grate-

ful to the students for their feedback and suggestions. We also thank all

our colleagues who helped gather the problems of Part I. The teaching assis-

tants when Yves Robert was teaching the Algorithms course were (ordering by

year) Odile Millet-Botta, Tanguy Risset, Alain Darte, Bruno Durand, Fr´ed´eric

Vivien, Jean-Christophe Dubacq, Olivier Bodini, Daniel Hirschkoﬀ, Matthieu

Exbrayat, Natacha Portier, Emmanuel Hyon, Eric Thierry, Michel Morvan,

and Yves Caniou. The teaching assistants when Anne Benoit took over were

(ordering by year) Victor Poupet, Damien Regnault, Benjamin Depardon,

Jean-Fran¸cois Pineau, Cl´ement Rezvoy, Christophe Mouilleron, Fanny Du-

foss´e, and Anne-C´ecile Orgerie.

We also wish to thank the following people who have contributed to some

of the content by their insightful suggestions, their own previously published

work, or their help reviewing draft chapters: Guillaume Aupy, Marin Bougeret,

Jean-Yves l’Excellent, Arnaud Legrand, Loris Marchal, Paul Renaud-Goud,

Veronika Sonigo, and Bora U¸car.

Finally, a word of caution on bibliographical notes: Some exercises have ap-

peared in many sources, and the references that we give may well not be the

original ones. Also, the absence of any reference is not a claim for originality!

However, all solutions are ours, and they have been tested and veriﬁed by the

students at ENS Lyon, the teaching assistants, and ourselves (but we keep the

sole responsibility for errors). We welcome comments and suggestions to our

e-mail addresses.

Anne Benoit, Anne.Benoit@ens-lyon.fr

Yves Robert, Yves.Robert@ens-lyon.fr

Fr´ed´eric Vivien, Frederic.Vivien@inria.fr

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