Distributed Computing Through Combinatorial Topology

I. Fundamentals 1. Introduction 2. Two-Process Systems 3. Elements of Combinatorial Topology

II. Colorless Tasks 4. Colorless Wait-free Computation 5. Solvability of Colorless Tasks 6. Byzantine Colorless Computation 7. Simulations and Reductions

III. General Tasks 8. Read-Write Protocols for General Tasks 9. Manifold Protocols 10. Connectivity 11. Wait-Free Computability for General Tasks

IV. Advanced Topics 12. Renaiming and Oriented Manifolds 13. Task Solvability in Different Communication Models 14. Colored Simulations and Reductions 15. Classifying Loop Agreement Tasks 16. Immediate Snapshot Subdivisions

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.

"...very well-written. All the figures, examples, and illustrations serve nicely to explain various concepts...mathematicians and computer scientists both would equally benefit from this book...a new researcher in this area would find this book very helpful" --SIGACT News

"...the first systematic exposition of an approach to distributed computing based on tools of combinatorial topology.a valuable addition to the existing literature, it will be appreciated by many different categories of readers including university students and researchers in computers science as well as topologists interested in practical applications." --Zentralblatt MATH

"This outstanding book...explores the connections between distributed computation and topology in detail...systematically organizes material that previously was only available across a collection of conference and journal publications with inconsistent notations and terminology..." --Computing Reviews

"...there has not been a monograph that comprehensively covers the intersection of topology and distributed computing...This book thus finds its place for filling precisely this niche, and will be welcomed by readers..." --Computing Reviews, July 24 2014

"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