Exact and Approximate Median Splitting on Distributed Memory Machines

We present in this paper a new fine grained median split algorithm which places the median on the middle index of an input array of size N . Running on P processors, the randomized version converges in O ( N P × (log(N) + μ) ) average time where 0 < P < N4 and μ is the time to swap a pair of elements between two nodes. At each iteration, the nodes process only its local elements and exchange part of them with another processor of the network. This makes it a decentralized parallel algorithm and offers the possibility to take advantage of massively parallel computing networks based on distributed memory systems.