Minimal Size of Piggybacked Information for Tracking Causality: A Graph-Based Characterization

Abstract

A fundamental problem in distributed computing consists in tracking causal dependencies between relevant events occurring during the computation, named observable events. Several methods have been proposed so far in order to track these dependencies on line. They require to propagate information among processes participating in the computation, by piggybacking additional control data to the computation messages. All these methods have to face the problem of the size of piggybacked information that could become prohibitive. However, bounding the size of piggybacked information may lead to the irremediable loss of causal dependencies, if the set of observable events is not correctly chosen. The challenge is to determine the minimal size of piggybacked information, in function of a given set of observable events, allowing to track all causal dependencies. This paper provides an answer to this previously open problem. This answer is based on the construction of a weighted graph modelizing the given computation with its observable events. Although the minimal value can be known only when all the computation is known, it can be used off line to perform a posteriori analysis of a computation.