We revisit the classical problem of the reduction collective operation in a heterogeneous environment. We discuss and evaluate four algorithms that are non-clairvoyant, i.e., they do not know in advance the computation and communication costs. On the one hand, \bins and \fibo are static algorithms that decide in advance which operations will be reduced, without adapting to the environment; they were originally defined for homogeneous settings. On the other hand, \dyn and \dynnc are fully dynamic algorithms, for commutative or non-commutative reductions. With identical computation costs, we show that these algorithms are approximation algorithms. When costs are exponentially distributed, we perform an analysis of \dyn based on Markov chains. Finally, we assess the relative performance of all four non-clairvoyant algorithms with heterogeneous costs though a set of simulations.
