Lower bounds on parallel algorithms for finding the first maximal independent set (Q1072703)

In this paper we introduce a model of computation using oracles which allows us to consider a class of problems which involve selecting a subset of a set of elements. This class can be solved in linear sequential time, but we prove that any deterministic or probabilistic parallel algorithm using p processors can achieve a speedup of at most O(log p). In addition, we prove that any algorithm that solves this class of problems must have a specific sequential structure.