This is a superb book. I taught a graduate level course based on it at Lehigh University in 1984 or 1985. It was awarded the prestigious annual Lanchester prize for book of the year Operations Research Society of America about that time. Robert Tarjan was awarded the ACM's Turing award, computer sciences closest equivalent to the Nobel Prize for his contibutions to the theory of algorithms. This book is an excellent introduction to his work. The algorithms in this book were state of the art when it was published, but I don't know how close they are to today's best.
Most of the optimal algorithms in the book grew out of Tarjan's pioneering work on algorithms that minimizes total complexity by allowing individual chunks of work to consume large amounts of computing resources if they build up "credits" that make subsequent steps more efficient. Until Tarjan used this approach to develop superior algorithms for a number of classical problems, the state of the art had been to limit the resources consumed by each step and bound total complexity by multipying the number of steps by the worst case resource consumption per step.
Tarjan's exposition illustrates the power of abstraction. He uses abstract data types throughout, carefully defining them in terms of their fundamental operations. This approach will be very natural for anyone familiar with object oriented programming.
There is a huge amount of information in very few pages, but it is organized very well. Often Tarjan's carefully chosen words say a lot more than is apparent to casual reader's. I spent one 75 minute period explaining his 12 line proof of one of his algorithms. Then the class demanded that I illustrate how the algorithm actually worked on a real problem, so we spent another 1.5 classes applying the algorithm to a small problem I contrived to exercise all of its boundary conditions.
Other faculty advised me that this book was much too hard for course intended for advanced undergraduate and beginning graduate students, but the students disagreed. More than one commented that the material was hard after first reading, but that after hearing my lectures and rereading their assignments, they realized that it was really pretty easy and that the book presented it well. Most would have appreciated worked out examples to observe the dynamic behavior of the algorithms. One student animated some of the algorithms and went on to write his masters thesis on algorithm animation.
