M Pivot Sort Faster Than Quick Sort

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M Pivot Sort Faster Than Quick Sort!

• Presenter James Edmondson
• Mentor Dr. Judy Hankins
• Study funded by MTSU Ronald E McNair Program

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M Pivot Sort Faster than Quick Sort!
Table of Contents

• Introduction .
• Introduction to M Pivot Sort..
• Testing System Specifications
• Testing Ascending Lists
• Testing Descending Lists.
• Testing Random Integer Lists.
• Testing Random String Lists
• Testing Random Class Lists
• Conclusion...
• References..

3 5 7 8 10 12 15 17 19 20
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M Pivot Sort Faster than Quick Sort!
Introduction

• Sorting Algorithms
• Sorting algorithms constitute the core of most
  algorithm textbooks.
• Most computer programmers still use sorting
  algorithms that were developed in the late 1950s
  and early 1960s.
• O(n log n) is the theoretical lower bound for
  comparison based sorting algorithms.
• New O(n log n) algorithms have been developed as
  late as Multikey Quick Sort in 1997 but are
  usually specialized sorts for certain types of
  data.

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M Pivot Sort Faster than Quick Sort!
Introduction

• Sorting Algorithms (continued)
• To be accepted into common practice, new sorting
  algorithms have to compete with Quick Sort in
  speed and usability.
• Two other algorithms, Merge Sort and Heap Sort,
  are also used widely and should be included in
  empirical comparisons.

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M Pivot Sort Faster than Quick Sort!
Introduction M Pivot Sort

• M Pivot Sort
• Based on partitioning principle in Quick Sort.
• Applies the Strong Law of Large Numbers to
  produce better sampling than Quick Sort.
• Handles duplicates in linear time (Quick Sort
  goes into polynomial time without three way
  partitioning.)
• Performs on average in O(n log n) time.
• Has a better worst case scenario (roughly half)
  than Quick Sort.

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M Pivot Sort Faster than Quick Sort!
Introduction M Pivot Sort

• M Pivot Sort (continued)
• Performs more targeted moves than Quick Sort
  (results in less moves)
• Performs slightly more data comparisons than
  Quick Sort but far less than Heap Sort.
• Performs less recursion than Quick Sort or Merge
  Sort.
• May perform runtime changes to correct polynomial
  time O(n2) performance by changing the number
  of pivots (3-7).

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M Pivot Sort Faster than Quick Sort!
Testing System Specifications

• System Specifications for Testing
• Quad Xeon, 2 GBs of RAM, Intel Architecture.
• Windows 2003 Server Standard Edition.
• Visual C command prompt based.
• Random Integer Generator designed by Andy Thomas.
• Random string generator produces 4-19 character
  random ANSI C strings.
• Random class generator produces 4 7-17 character
  random ANSI C strings, one of which is the
  sorting key.
• Ascending and descending lists are integer based.
• Ten different sets of data ran for each algorithm
  for each type of test. Mean average taken for
  stats generated here.

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M Pivot Sort Faster than Quick Sort!
Testing Ascending Lists
Tests on list of 100 million ascending integers
Units expressed in 100 million operations, ie
Merge Sort performed 66.83 100 million
operations, or 6,683,000,000 total operations.
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M Pivot Sort Faster than Quick Sort!
Testing Ascending Lists
Tests on list of 100 million ascending integers
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M Pivot Sort Faster than Quick Sort!
Testing Descending Lists
Tests on list of 100 million descending integers
Units expressed in 100 million operations, ie
Merge Sort performed 66.83 100 million
operations, or 6,683,000,000 total operations.
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M Pivot Sort Faster than Quick Sort!
Testing Descending Lists
Tests on list of 100 million descending integers
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M Pivot Sort Faster than Quick Sort!
Testing Random Integers
Tests on list of 100 million random integers
Units expressed in 100 million operations, ie
Merge Sort performed 78.65 100 million
operations, or 7,650,000,000 total operations.
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M Pivot Sort Faster than Quick Sort!
Testing Random Integers
Tests on list of 100 million random integers
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M Pivot Sort Faster than Quick Sort!
Testing Random Integers
Test on list of 100 million random integers
(200,000 possible values duplicate records
present)
Shows Quick Sorts performance on duplicates vs.
Pivot Sort. Source is M Pivot Sort Replacing
Quick Sort.
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M Pivot Sort Faster than Quick Sort!
Testing Random Strings
Tests on list of 10 million random strings
Units expressed in 10 million operations, ie
Merge Sort performed 68.65 10 million operations,
or 686,500,000 total operations.
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M Pivot Sort Faster than Quick Sort!
Testing Random Strings
Tests on list of 10 million random strings
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M Pivot Sort Faster than Quick Sort!
Testing Random Classes
Tests on list of one million random classes
Units expressed in 1 million operations, ie Merge
Sort performed 58.58 one million operations, or
58,580,000 total operations.
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M Pivot Sort Faster than Quick Sort!
Testing Random Classes
Tests on list of one million random classes
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M Pivot Sort Faster than Quick Sort!
Conclusion

• Conclusion
• M Pivot Sort meets or beats the time taken by
  Quick Sort for sorts on contiguous lists
  (arrays).
• M Pivot Sort performs favorably on sorting
  presorted and descending lists (common database
  operations.)
• M Pivot Sort performs less moves and less total
  operations than Quick Sort, Heap Sort, and Merge
  Sort.
• M Pivot Sort is an ideal candidate for general
  purpose sorting libraries for varied or singular
  data types.

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M Pivot Sort Faster than Quick Sort!
References

• References
• 1 Bentley, Jon L. The trouble with qsort.
  UNIX Review. 10.2 (1992) 85-90.
• 2 Bentley, Jon L. Software Exploratorium
  history of a Heapsort. UNIX Review. 10.8
  (1992) 71-77.
• 3 Cormen, Thomas, et al. Introduction to
  Algorithms. 2nd ed. Massachusetts MIT Press,
  2001.
• 4Edmondson, James. M Pivot Sort Replacing
  Quick Sort. Proceedings of the 2005
  International Conference on Algorithmic
  Mathematics and Computer Science (2005) 47-53.
• 5 Kruse, Robert, et al. Data Structures
  Program Design in C . 2nd ed. New Jersey
  Prentice Hall, 1997. 335.
• 6 McClave, James T. and Terry Sincich. A First
  Course in Statistics Annotated Instructors
  Edition. 8th ed. New Jersey Prentice Hall,
  2003. 224, 277-308.
• 7 Sedgewick, Robert and Jon Bentley.
  Quicksort is Optimal. Knuthfest, Stanford
  University, Stanford. January 2002.
• 8 Sedgewick, Robert. Algorithms in Java. 3rd
  ed. Boston Addison-Wesley, 2003.
• 9 Thomas, Andy. Randomal64 Pseudo Random
  Number Generator. Generation5.org. 20 April
  2001. 6 Feb. 2005 lthttp//www.generation5.org/cont
  ent/2001/ga01.aspgt.