Pcm- Omars Algorithm: Parallel Computation of Median - Omniscient Maximal Reduction Steps

Abstract

The goal of a distributed computation algorithm is to determine the result of a function of numerical elements, which are distributed in n multi sets.It is known that computation of holistic aggregation functions on distributed multi sets indeed requires more work than non holistic aggregation functions. But with this article we will prove that the computation of a holistic function, which named exact median, can be computed efficiently by providing both a candidate finding and a deterministic location algorithms which computes the position of exact median, dispelling the misconception that solving distributed median computation through parallel aggregation is infeasible. Some of most important part in Big Data field is to evaluate massive data values. A special case in this field is the calculation of kthsmallest values (specially the median) of distributed multi sets containing enormous data. Many approximation algorithms and algorithms with iterative or recursive steps of determination of median give solutions for the computation of median. But firstly sometime approximate value is dangerous for some data evaluation projects or researchs and secondly with other algorithms, the data blocking time is too long through the iteration or the recursion between global node and local nodes. This article focuses on a solution that gives a best effectively computation for this problem named PCM-oMaRS algorithm. The PCM-oMaRS algorithm guarantees the maximal reduction steps of the computation of the exact median in distributed multi sets and proves that we can compute the exact median effectively without needing the usage of recursive or iterative methods at the global communication level, which reduces the blocking time maximally. This algorithm provides more efficient execution not only in distributed multi sets even in local multi set with enormous data.