Asynchrony and Delay-Sensitive Bounds

In this chapter our goal is to obtain complexity bounds for work-efficient message-passing algorithms for the Do-All problem. We require that the al- gorithms tolerate any pattern of processor crashes with at least one surviving processor. More significantly, we are interested in algorithms whose work de- grades gracefully as a function of the worst case message delay d. Here the requirement is that work must be subquadratic in n and p as long as d = o(n). Thus for our algorithms we aim to developdelay-sensitive analysis of work and message complexity. Noting again that work must be Ω(p · n) for d ≥ n, we give a comprehensive analysis for d < n, achieving substantially better