by Lance Fortnow
We don't often present books that are aimed at more of the mass market in our reading lists, but this title is an entertaining discussion of the
NP problem. If your path to programming did not take you through computer science, the problem might appear obscure: How do you find the solution to a problem that allows many, many solutions and know it to be optimal. The canonical example is the traveling salesman problem: Given a journey that requires, say, stops at 30 customers, what is the shortest route to take? These problems, which involve examining more possibilities than the fastest computer could solve in centuries, are the
NP group. The central question is whether there is some as yet unknown solution to them that will allow them to be approached and solved in shorter time frames as we do with other, conventional (
Fortnow explains (in non-technical terms) how very different technology would be if it can be shown that
P = NP, meaning that all
NP problems are tractable within a reasonable time period. He demonstrates that even if
P != NP, related problems can be solved with "good enough" solutions. To wit, GPS systems will often find the shortest routes between two points. He also points out that the intractability of
NP problems is what allows us to do many forms of encryption. Finally, he gives an overview of the various research paths into the problem.
The book is an easy read and, to a technical eye, will seem longer than necessary. It also has some embarrassingly sloppy moments ("…a typical laptop can process about a trillion operations a second…"), but, in the main, it presents the problem and possible solutions clearly and entertainingly. It's good, light, vacation reading.