The Golden Ticket: P, NP, and the Search for the Impossible

by Lance Fortnow

Overview

The computer science problem whose solution could transform life as we know it

The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

Product Details

ISBN-13:	9780691175782
Publisher:	Princeton University Press
Publication date:	02/28/2017
Pages:	192
Sales rank:	662,374
Product dimensions:	6.00(w) x 9.10(h) x 0.60(d)

About the Author

Lance Fortnow is professor and chair of the School of Computer Science at Georgia Institute of Technology and the founder and coauthor of the Computational Complexity blog.

Table of Contents

Preface ix
Chapter 1 The Golden Ticket 1
Chapter 2 The Beautiful World 11
Chapter 3 P and NP 29
Chapter 4 The Hardest Problems in NP 51
Chapter 5 The Prehistory of P versus NP 71
Chapter 6 Dealing with Hardness 89
Chapter 7 Proving P ≠ NP 109
Chapter 8 Secrets 123
Chapter 9 Quantum 143
Chapter 10 The Future 155
Acknowledgments 163
Chapter Notes and Sources 165
Index 171

What People are Saying About This

From the Publisher

"You will love this book. It's completely accessible and captures the thrill, potential, and heartbreak of an edgy mathematical problem in terms that nonmathematicians will appreciate. After readingThe Golden Ticket, I sort of hope P isn't NP after all."—Vint Cerf, Internet Pioneer

"The P-NP problem is fundamental to computer science, and indeed all of mathematics. This book presents an engaging exposition of the problem, its history, and importance. In the process, it touches on major topics appearing in university computer science courses, all presented in an amusing style requiring no background in mathematics beyond the ability to solve Sudoku puzzles. I highly recommend it."—Stephen Cook, formulator of the P-NP problem

"This book, written by a world-class master of the field, is a grand tour of the most celebrated and profound unsolved problem in computer science. Fortnow's many ingenious explanations make the mysteries of computational complexity accessible to anyone interested in the fundamental questions: what can be computed and how fast can we compute it?"—John MacCormick, author of Nine Algorithms That Changed the Future

"This book is meticulous. Fortnow has really tracked down the history and background of this important and timely subject. Even complexity theorists will benefit from his fine scholarship. The Golden Ticket is the first of its kind—a book for general readers about complexity theory."—William Gasarch, University of Maryland

"Nobody explains the importance of the P-NP problem better than Fortnow."—William J. Cook, author of In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation

Editorial Reviews

"The Golden Ticket does a good job of explaining a complex concept in terms that a secondary-school student will understand—a hard problem in its own right, even if not quite NP."

Physics World

"Thoroughly researched and reviewed. Anyone from a smart high school student to a computer scientist is sure to get a lot of this book. The presentation is beautiful. There are few formulas but lots of facts."

Daniel Lemire's Blog

"A provocative reminder of the real-world consequences of a theoretical enigma."

Booklist

"One of Amazon.com’s 2013 Best Science Books"

One of Choice's Outstanding Academic Titles for 2013

Honorable Mention for the 2013 PROSE Award in Popular Science & Mathematics, Association of American Publishers

"As Fortnow describes. . . P versus NP is ‘one of the great open problems in all of mathematics' not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, ‘from cures to deadly diseases to the nature of the universe,' even ‘an algorithmic process to recognize greatness.'. . . To postulate that P ≠ NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration—but also of discovery and inquiry, of pleasures pleasingly delayed."—-Alexander Nazaryan, New Yorker

From the Publisher

"The Golden Ticketis an extremely accessible and enjoyable treatment of the most important question of theoretical computer science, namely whether P is equal to NP."

Choice

This awkward but eager work introduces readers to one of the most complicated problems in mathematics. P-type problems have a single solution and can be solved easily by computer, whereas NP, or “nondeterministic polynomial” problems, involve finding the relative “best” of numerous possible answers. NP problems include map-coloring puzzles, traveling-salesman puzzles (which seek to find the best combinations of routes between locations), and clique problems, like finding the largest group of people on Facebook who are all friends of each other. Fortnow’s “Golden Ticket” would be proof that P=NP, the discovery of efficient ways to solve NP-type problems. Whoever solves this decidedly nontrivial problem—one of the Clay Institute for Mathematics’ six unsolved “Millennium Problems”—will receive a million prize. In addition to exploring the actual quandary, Fortnow, chair of the Georgia Institute of Technology’s school of computer science, lays out a quick modern history of mathematical problem solving, and enthuses over the possibilities of a “beautiful world” where P=NP: the ability to quickly sequence DNA, cure cancer and AIDs, and predict the weather. Despite moments of notational confusion—what exactly do “P H NP,” “P W NP,” and “P M NP” mean?—Fortnow effectively initiates readers into the seductive mystery and importance of P and NP problems. 41 halftones, 41 line illus. (Apr.)

Publishers Weekly

"A provocative reminder of the real-world consequences of a theoretical enigma."

Booklist

[The Golden Ticket] is a book on a technical subject aimed at a general audience. . . . Lance's mix of technical accuracy with evocative story telling works.

Michael Trick's Operations Research Blog - Michael Trick

A great book. . . . [Lance Fortnow] has written precisely the book about P vs. NP that the interested layperson or IT professional wants and needs.

Shtetl-Optimized blog - Scott Aaronson

Fortnow's book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science.

Commercial Dispatch - Rob Hardy

The definition of this problem is tricky and technical, but in The Golden Ticket, Lance Fortnow cleverly sidesteps the issue with a boiled-down version. P is the collection of problems we can solve quickly, NP is the collection of problems we would like to solve. If P = NP, computers can answer all the questions we pose and our world is changed forever. It is an oversimplification, but Fortnow, a computer scientist at Georgia Institute of Technology, Atlanta, knows his stuff and aptly illustrates why NP problems are so important.

New Scientist - Jacob Aron

[This] as-yet-unsolved problem—identified by mathematicians as the P-NP problem—raises fundamental questions about just how far society can ride the technological wave triggered by the computer revolution. Fortnow unfolds a fascinating dual-track story of how this problem first emerged, Western researchers encountering it while trying to maximize computer efficiency, Russian analysts confronting it while puzzling over the persistent need for perebor ('brute force search'). Readers watch as the P-NP problem attracts investigators in cryptography, biology, quantum physics, and social networking—and frustrates them all. Fortnow allows nonspecialist readers to glimpse the conceptual difficulties here (try 'nondeterministic polynomial time,' for example). But he mercifully frames his discussion largely in nontechnical terms. Even readers averse to mathematics will share in the intellectual stimulation of pondering a riddle compelling us to ask what we should hope for—and fear—in replacing human brains with computer algorithms. A provocative reminder of the real-world consequences of a theoretical enigma.

Booklist - Bryce Christensen

As Lance Fortnow describes in his new book, The Golden Ticket: P, NP and the Search for the Impossible, P versus NP is 'one of the great open problems in all of mathematics' not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, 'from cures to deadly diseases to the nature of the universe,' even 'an algorithmic process to recognize greatness.'. . . To postulate that P ≠ NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration—but also of discovery and inquiry, of pleasures pleasingly delayed.

New Yorker - Alexander Nazaryan

In his first book-length foray into popular science, Fortnow (computer science, Georgia Inst. of Technology) tackles one of the biggest open problems in mathematics. P vs. NP can be succinctly phrased as the issue of whether some of the hardest and most important questions in mathematics have easily computable solutions. The questions themselves can range from how best to match up organ donors and recipients to how one can use the smallest number of different colors when creating a map. Without bringing formulas or computer code into the narrative, Fortnow sketches the history of this class of questions, convincingly demonstrates their surprising equivalence, and reveals some of the most far-reaching implications that a proof of P = NP would bring about. These might include tremendous advances in biotechnology (for instance, more cures for cancer), information technology, and even the arts. VERDICT Through story and analogy, this relatively slim volume manages to provide a thorough, accessible explanation of a deep mathematical question and its myriad consequences. An engaging, informative read for a broad audience.—J.J.S. Boyce, Manitoba Métis Federation

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