# Distributed Computing Through Combinatorial Topology

## Maurice Herlihy, Sergio Rajsbaum

Language: English

Pages: 336

ISBN: 0124045782

Format: PDF / Kindle (mobi) / ePub

*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.

- Named a 2013 Notable Computer Book for Computing Methodologies by
*Computing Reviews* - Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding
- Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols
- Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises

125. Neda Armando C, Herlihy Maurice, Rajsbaum Sergio. An equivariance theorem with applications to renaming. In: Proceedings of the 10th latin American international conference on theoretical informatics, LATIN’12. Berlin, Heidelberg, Germany: Springer-Verlag; 2012;133–144. 126. Novikov PS. On the algorithmic unsolvability of the word problem in group theory. Trudy Mat Inst Steklov. 1955;44:3–143. 127. Rabin Michael O. Recursive unsolvability of group theoretic problems. Ann Math.

surprisingly, immediate snapshots do not affect task solvability. It is well known (see Section 4.4, “Chapter Notes”) that one can construct a wait-free snapshot from single-word reads and writes, and we will see in Chapter 14 how to construct a wait-free immediate snapshot from snapshots and single-word write instructions. It follows that any task that can be solved using immediate snapshots can be solved using single-word reads and writes, although a direct translation may be impractical. In

uses a simulation argument to prove the equivalence of -resilient and wait-free consensus protocols using shared objects. Exercise 7.1 is based on Afek, Gafni, Rajsbaum, Raynal, and Travers [4], where reductions between simultaneous consensus and set agreement are described. 7.7 Exercises Exercise 7.1 In the -simultaneous consensus task a process has an input value for independent instances of the consensus problem and is required to decide in at least one of them. A process decides a pair ,

course this program is just a readable way to specify a protocol complex. Figures 9.10 and 9.11 shows the control structure and pseudo-code to implement weak symmetry breaking using set agreement. The processes share an -element array of input names, chosen[·], whose entries are initially (Line 3). The processes also share a set agreement protocol instance (Line 4). Each process calls the set agreement object’s decide()method, using its own input name as input, and stores the result in

Figure 12.6 Standard orientation for Ch . Here there are three processes, so , and one round of execution, so . The orientation of the central simplex marked is therefore . Figure 12.7 Orientation for a 1-dimensional subdivision. An internal simplex of is one that contains no boundary vertices. Lemma 12.4.4 If all internal vertices are colored 0, then the content of the internal simplices is . Proof Let be the binary coloring that assigns to every vertex on the boundary and to every