Compositional competitiveness for distributed algorithms

We define a measure of competitive performance for distributed algorithms based on throughput, the number of tasks that an algorithm can carry out in a fixed amount of work. This new measure complements the latency measure of Ajtai et al., which measures how quickly an algorithm can finish tasks that start at specified times. The novel feature of the throughput measure, which distinguishes it from the latency measure, is that it is compositional: it supports a notion of algorithms that are competitive relative to a class of subroutines, with the property that an algorithm that is k-competitive relative to a class of subroutines, combined with an l-competitive member of that class, gives a combined algorithm that is kl-competitive. In particular, we prove the throughput-competitiveness of a class of algorithms for collect operations, in which each of a group of n processes obtains all values stored in an array of n registers. Collects are a fundamental building block of a wide variety of shared-memory distributed algorithms, and we show that several such algorithms are competitive relative to collects. Inserting a competitive collect in these algorithms gives the first examples of competitive distributed algorithms obtained by composition using a general construction.Comment: 33 pages, 2 figures; full version of STOC 96 paper titled "Modular competitiveness for distributed algorithms.

Counting networks

... replied the businessman. \I count them and recount them. It is di cult but I am a man who is naturally interested in matters of consequence." |Antoine de Saint-Exupery, The Little Prince The counting problem requires n asynchronous processes to assign themselves successive values. A solution is linearizable if the order of the values assigned re ects the real-time order in which they were requested. Linearizable counting lies at the heart of concurrent time-stamp generation, as well as concurrent implementations of shared counters, FIFO bu ers, and similar data structures. We consider solutions to the linearizable counting problem in a multiprocessor architecture in which processes communicate by applying read-modify-write operations to a shared memory. Linearizable counting algorithms can be judged by three criteria: the memory contention produced, whether processes are required to wait for one another, and how long it takes a process to choose a value (the latency). A solution is ideal if it has low contention, low latency, and it eschews waiting. The conventional software solution, wher