Abstract
Sorting an array of n elements represents one of the leading problems in different fields of computer science such as databases, graphs, computational geometry, and bioinformatics. A large number of sorting algorithms have been proposed based on different strategies. Recently, a sequential algorithm, called double hashing sort (DHS) algorithm, has been shown to exceed the quick sort algorithm in performance by 10–25%. In this paper, we study this technique from the standpoints of complexity analysis and the algorithm’s practical performance. We propose a new complexity analysis for the DHS algorithm based on the relation between the size of the input and the domain of the input elements. Our results reveal that the previous complexity analysis was not accurate. We also show experimentally that the counting sort algorithm performs significantly better than the DHS algorithm. Our experimental studies are based on six benchmarks; the percentage of improvement was roughly 46% on the average for all cases studied.
Highlights
Sorting is a fundamental and serious problem in different fields of computer science such as databases [1], computational geometry [2, 3], graphs [4], and bioinformatics [5]
The third aspect refers to proving that the double hashing sort (DHS) algorithm exhibits a lower level of performance than another certain algorithm from a practical point of view. The results of these studies are as follows: (1) the previous complexity analysis of the DHS algorithm was not accurate; (2) we calculated the corrected analysis of the DHS algorithm; (3) we proved that the counting sort algorithm is faster than the DHS algorithm from theoretical and practical points of view
The sorting problem is to rearrange the elements of a given array in increasing order
Summary
Sorting is a fundamental and serious problem in different fields of computer science such as databases [1], computational geometry [2, 3], graphs [4], and bioinformatics [5]. The second note is that the calculated running time for the worst case is not correct if the value of n is large and m is small This situation implies that the number of repetitions in the input array is large because the n elements of the input array belong to a small range. The value of m is small compared with the input size n; the array contains many repeated elements In this case, the maximum number of slots is m, and there is no need to map the elements of the input array to n slots such as mapping sort algorithm [20], where the index of the element ai is calculated using the equation: ⌊((ai − Min(A)) × n)/(Max(A) − Min(A))⌋. Each pair of bar represents the running times for the CS and DHS algorithms using a
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