With refinements to the WEAK-HEAPSORT...

With refinements to the WEAK-HEAPSORT algorithm we establish the general and practical relevant sequential sorting algorithm RELAXED-WEAK-HEAPSORT executing exactly ndlog ne#2 dlog ne + 1 # n log n # 0:9n comparisons on any given input. The number of transpositions is bounded by n plus the number of comparisons. Experiments show that RELAXED-WEAK-HEAPSORT only requires O(n) extra bits. Even if this space is not available, with QUICK-WEAK-HEAPSORT we propose an efficient QUICKSORT variant with n log n+0:2n+ o(n) comparisons on the average. Furthermore, we present data showing that WEAK-HEAPSORT, RELAXED-WEAK-HEAPSORT and QUICKWEAK-HEAPSORT beat other performant QUICKSORT and HEAPSORT variants even for moderate values of n.

Abstract: Problem statement: Several efficient algorithms were developed to cope with the popular task of sorting. Improved heap sort is a new variant of heap sort. Basic idea of new algorithm is similar to classical Heap sort algorithm but it builds heap in another way. The improved heap sort algorithm requires nlogn-0.788928n comparisons for worst case and nlogn-n comparisons in average case. This algorithm uses only one comparison at each node. Hardware has impact on performance of an algorithm. Since improved heap sort is a new algorithm, its performance on different hardware is required to be measured. Approach: In this comparative study the mathematical results of improved heap sort were verified experimentally on different hardware. To have some experimental data to sustain this comparison five representative hardware were chosen and code was executed and execution time was noted to verify and analyze the performance. Results: Hardware impact was shown on the performance of improved heap sort algorithm. Performance of algorithm varied for different datasets also. Conclusion: The Improved Heap sort algorithm performance was found better as compared to traditional heap sort on different hardware, but on certain hardware it was found best. Key words: Complexity, performance of algorithms, sorting