Collective asynchronous reading with polylogarithmic worst-case overhead

The Collect problem for an asynchronous shared-memory system has the objective for the processors to learn all values of a collection of shared registers, while minimizing the total number of read and write operations. First abstracted by Saks, Shavit, and Well, Collect is among the standard problems in distributed computing, The model consists of n asynchronous processes, each with a single-writer multi-reader register of a polynomial capacity. The best previously known deterministic solution performs script O sign(n^3/2 log n) reads and writes, and it is due to Ajtai, Aspnes, Dwork, and Waarts. This paper presents a new deterministic algorithm that performs script O sign(n log⁷ n) read/write operations, thus substantially improving the best previous upper bound. Using an approach based on epidemic rumor-spreading, the novelty of the new algorithm is in using a family of expander graphs and ensuring that each of the successive groups of processes collect and propagate sufficiently many rumors to the next group. The algorithm is adapted to the Repeatable Collect problem, which is an on-line version. The competitive latency of the new algorithm is script O sign(log⁷ n) vs. the much higher competitive latency script O sign(√n log n) given in [3]. A result of independent interest in this paper abstracts a gossiping game that is played on a graph arid that gives its payoff in terms of expansion.