"Analysis and optimization of a kchain reduction algorithm for
distributed computer systems" Kurnosov M.G. 
In the LogP model of parallel computing, an analytical expression of the kchain algorithm's execution time is derived. The optimal value of k in the LogP model is found. A new algorithm based on the optimal value of k is developed. For the reduction of root process's waiting time, an algorithm with an adaptive number of chains is proposed. The dependence of the execution time of the proposed algorithm on the number of processes has a growth rate of Ο(sqrt{P}), which is more efficient compared to the linear running time of the original kchain algorithm. The proposed algorithms are implemented in the MPI standard and studied on computer clusters with InfiniBand QDR networks. Keywords: root reduction, message passing models, MPI, parallel programming, distributed computer systems.

