Dimitri P Bertsekas | Dimitri P. Bertsekas
1 Challenging & Succesful Treatment of the Subject
Bertsakas's Network Optimization is probably the most challenging graduate textbook on network flows and optimization. Besides the chapters on classical subjects as shortest path or max-flow/min-cost problems, (which are very rigorously dealt despite their very standard nature of the subjects) I've found especially the Auction Algorithms chapter very throughout and inspiring. The next chapters, Nonlinear Network Optimization and Network Problems with Integer Constraints also are good; these are not usually included in other graduate network optimization books. In each chapter, Author digs into almost all theorems, propositions or notions and don't miss the related proofs or demonstrations, which is usually omitted in other books. I guess it is an important feature for those who want to see theoretical background of the subjects. Its bibliography is very rich and sufficiently up-to-date (until 1997, not bad since it is printed at 1998!). I've found the exercises very challenging, one should consume a very lot of time to do the necessary proofs. These are not as numerous as in Bazaraa's or Ahuja's books, but their quality is by far superior; the author hasn't filled the book with the standard/classical exercises which can be found in all books. Since it deals in detail with the theory, the presentation of the subjects sometimes appears difficult to capture. I also advise to get the errata from book's homepage since it may create sometimes difficulties. The graph theory notions come usually omitted in the book, so one may need a graph theory title to accompany it. Also its appendix that contains a mathematical review somewhat less extensive than in his "Nonlinear Programming" book (almost a separate monograph!), which I recommend highly also. Thus the book comes devoted and concentrated solely on the Network Optimization theory and algorithms, and in my opinion, it became highly successful. I strongly believe that may become the standard title on the subject of the following years. For those who may find its presentation difficult, I suggest to use it along with Ahuja's "Network Flows" which has a more general structure and presentation. But I found the book clearly superior to that book or Bazaraa's "Linear Programming and Network Flows" whose Network Flows chapters are messy. Finally I may say, it is a highly successful book is very worth of its price.
2 Lucid, well-illustrated study of network flows
This is a well-explained, well-illustrated introduction of some of the most important aspects of network flows. (Note: This is an Internet-centric review, even though the book is not about the Internet.) Although the treatment is theoretical rather than specific to the Internet, it is especially relevant now that traffic engineering is being applied to the Internet. Of course ATM and telephone networks have employed this for many years, but there is a need to go back to fundamentals when applying these concepts to the Internet (or other areas). The book starts with the shortest path problem, which is familiar to the Internet community. Then max-flow and min-cost problems are introduced. These are central to traffic engineering. Thereafter non-linear network flow optimization and discrete problems are attacked. Linear programming techniques such as the simplex method are also described. Is excellent training material for those having to wrestle with traffic engineering problems.
