Abstract
Parallel processing of algorithms is an effective way to achieve higher performance on multiprocessor systems rather. During parallelization, it is critical to minimize the difference between the processing time for threads. It is necessary to choose a method that can efficiently distribute the workload evenly across the threads. This paper deals with a special kind of nested loops where the internal loop iterator depends on the outer loop iterator. In such cases, the process can be represented as an upper (or lower) triangular matrix. This paper introduces a method for partitioning the outer loop according to the indices in an almost optimal manner, so that the partial loops in each thread will take nearly the same number of steps. In addition, we examine the potential of a perfect partition and try to determine the maximum (but still meaningful) partition size.
Highlights
There are multiple ways to find duplicated elements of a dataset, but in the cases where the size of the set drastically increases, simple sequential solutions have serious runtime limitations
The most common way to find duplicates is the brute force method, which compares each element to every other element in the dataset
If the R relation is ignored, that is, the brute force algorithm is used in the processing, for a set of 20 elements 400 comparisons (Figure 1.b.) are needed
Summary
There are multiple ways to find duplicated elements of a dataset, but in the cases where the size of the set drastically increases, simple sequential solutions have serious runtime limitations. The most common way to find duplicates is the brute force method, which compares each element to every other element in the dataset This solution has the time complexity of O(n2) and is rarely used in the real world. [17] An advanced version of this method considers that an element will always be self-consistent (reflexivity) and assumes that if an element is identical to the other, the inverse of the condition is satisfied (symmetricity), or necessarily (for a more general solution) transitivity is not allowed. Given these rules, we got a non empty S = ∅ set and a reflexive symmetric non-transitive R relation: ∀a ∈ S : (aRa). Because of non-transitivity, it will be necessary to traverse this upper triangle to find all duplication for each element
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