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.
Highlights
As Knuth describes in[1] theoretical lower bound for general sorting algorithms is: log (n!) = nlogn-n loge + θ(log n) ≈ nlogn – 1.442695nFor the worst-case numbers of comparisons, this lower bound makes sorting by merging, sorting by insertion and binary search very efficient.Cormen[2] describes Heap Sort is a divide and conquer algorithm that first orders keys in a binary heap and reorders the heap into sorted order.Heap sort was originally proposed by William in[3]
In[11] improvement of complexity was shown mathematically and this was verified on five different hardware test beds
The experiments were conducted on following Test beds: Test bed I: Celeron 2.5 GHz, 512 MB RAM, 40 GB HDD, Windows XP Professional with service Pack 2, Microsoft Visual C++ compiler
Summary
Floyd[4] improved William’s algorithm His algorithm uses 2n comparisons in the worst case to build a heap. McDiarmid and Reed proposed[7] a new variant of bottom up heap to reduce number of comparisons This algorithm uses 2 |_(n-1)/2 _| additional bits, 2 bits per internal nodes for storing three values u(unknown),l (left) and r(right). The request of placing the element in the root immediately to its destination is relaxed This new algorithm requires nlogn-0.788928n comparisons for worst-case and nlogn-n comparisons in average case which is only about 0.4n more than necessary. If it uses Gonnet and Munro’s[12] fastest algorithm for building heaps. The research was carried out to check the behavior of the algorithm on different platforms in comparison to other traditional algorithms
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