Distributed Computing Through Combinatorial Topology

Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further.

Table of Contents:
I. Fundamentals1. Introduction2. Two-Process Systems3. Elements of Combinatorial Topology II. Colorless Tasks4. Colorless Wait-free Computation5. Solvability of Colorless Tasks6. Byzantine Colorless Computation7. Simulations and Reductions III. General Tasks8. Read-Write Protocols for General Tasks9. Manifold Protocols10. Connectivity11. Wait-Free Computability for General Tasks IV. Advanced Topics12. Renaiming and Oriented Manifolds13. Task Solvability in Different Communication Models14. Colored Simulations and Reductions15. Classifying Loop Agreement Tasks16. Immediate Snapshot Subdivisions

About the Author :
Maurice Herlihy received an A.B. in Mathematics from Harvard University, and a Ph.D. in Computer Science from M.I.T. He has served on the faculty of Carnegie Mellon University, on the staff of DEC Cambridge Research Lab, and is currently a Professor in the Computer Science Department at Brown University. Dr. Herlihy is an ACM Fellow, and is the recipient of the 2003 Dijkstra Prize in Distributed Computing. He shared the 2004 Gödel Prize with Nir Shavit, with whom he also shared the 2012 Edsger W. Dijkstra Prize In Distributed Computing. Prof. Dmitry Kozlov is recipient of the Wallenberg Prize of the Swedish Mathematics Society (2003), the Gustafsson Prize of the Goran Gustafsson Foundation (2004), and the European Prize in Combinatorics (2005). He has been a Senior Lecturer at the Royal Institute of Technology, Stockholm, and an Assistant Professor at ETH Zurich. Currently he holds the Chair of Algebra and Geometry at the University of Bremen, Germany. He is the author of the book Combinatorial Algebraic Topology published by Springer Verlag in 2008. Prof. Sergio Rajsbaum is a member of the Institute of Mathematics at UNAM, where he is now a Full Professor. He has spent postdoctoral and sabbatical stays at the Massachusetts Institute of Technology and HP Research Labs. His main research interests are in the theory of distributed computing, and has about 100 publications in prestigious conferences and journals, and has been Program Committee member, and Program Chair of main forums in the area, such as the ACM Principles of Distributed Computing.

Review :
"In Distributed Computing, the modern mathematical field of Combinatorial Topology finally finds a natural application space. This book elucidates this intriguing connection through a series of well thought out examples, making complex computational phenomena and the deep theorems seem intuitive even to the beginner. I highly recommend it to anyone who is interested in the fundamentals of computing, since asynchrony, the key phenomena this book explains, is bound to dominate computation and communication in years to come." - Prof. Nir Shavit, Professor of Computer Science, Massachusetts Institute of Technology, Cambridge, MA "Written by the leading experts in this area, this book is a unique endeavor covering the exciting topic of understanding distributed computing through topology. The book will appeal to researchers in distributed computing and to mathematicians." - Prof. Hagit Attiya, Professor of Computer Science, Technion - Israel Institute of Technology "This book is a major contribution to distributed computing, integrated with algebraic topology. Based on the seminal work of the authors, it represents a collection of the most up-to-date results in the field, presented in a very progressive manner, from intuitions to detailed proofs and connections to fundamental mathematical concepts." - Eric Goubault, cea list and Ecole Polytechnique