Bead–Sort :: A Natural Sorting Algorithm
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The document describes a natural sorting algorithm called Bead-Sort that is inspired by observing beads falling through a frame. Bead-Sort can sort positive integers and has a time complexity that ranges from O(1) if all beads are dropped together, O(n) if beads are dropped row by row, or O(S) if each bead is dropped individually, where S is the sum of the input integers. The document also discusses three possible implementations of Bead-Sort as an analog hardware system, cellular automaton, or digital hardware.
Bead–Sort :: A Natural Sorting Algorithm
- 1. Bead–Sort: A Natural Sorting Algorithm Joshua J. Arulanandham, Cristian S. Calude, Michael J. Dinneen In The Bulletin of the European Association for Theoretical Computer Science 76 (2002)
- 2. Abstract Nature is not only a source of minerals and precious stones but is also a mine of algorithms. By observing and studying natural phenomena, computer algorithms can be extracted. In this note, a simple natural phenomenon is used to design a sorting algorithm for positive integers, called here Bead–Sort. The algorithm’s run–time complexity ranges from O(1) to O(S) (S is the sum of the input integers) depending on the user’s perspective. Finally, three possible implementations are suggested.
- 4. Time Complexity Time complexity of Bead–Sort can be evaluated at three different levels: ● ‘dropping all beads together’ as a single operation O(1) ● ‘dropping the row of beads’ in the frame (representing a number) O(n) ● ‘dropping each and every bead’ as a separate operation. O(S) where S is the sum of the input integers. Space n-square Only for positive integers
- 5. Implementation (Analog Hardware Implementation)
- 6. Implementation (Cellular Automaton Implementation)
- 7. Implementation (Digital Hardware Implementation)
- 8. QUESTIONS