Fun-sort--or the chaos of unordered binary search

Authors:
Therese Biedl;Timothy Chan;Erik D. Demaine;Rudolf Fleischer;Mordecai Golin;James A. King;J. Ian Munro
Affiliations:
Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1;Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1;MIT Laboratory for Computer Science, Cambridge, MA;Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1;Department of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Venue:
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
Year:
2004

Citing 6
Cited 4

Sorting on defective VLSI-arrays

Integration, the VLSI Journal
Randomized algorithms

Randomized algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching

The art of computer programming, volume 3: (2nd ed.) sorting and searching
Periodification scheme: constructing sorting networks with constant period

Journal of the ACM (JACM)
Partition Sorts for VLSI

GI - 13. Jahrestagung
Local Divergence of Markov Chains and the Analysis of Iterative Load-Balancing Schemes

FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science

Computational geometric aspects of rhythm, melody, and voice-leading

Computational Geometry: Theory and Applications
Sorting the slow way: an analysis of perversely awful randomized sorting algorithms

FUN'07 Proceedings of the 4th international conference on Fun with algorithms
The geometry of musical rhythm

JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Rotated library sort

CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141

Quantified Score

Hi-index	0.00

Visualization

Abstract

Usually, binary search only makes sense in sorted arrays. We show that insertion sort based on repeated "binary searches" in an initially unsorted array also sorts n elements in time Θ(n2 log n). If n is a power of two, then the expected termination point of a binary search in a random permutation of n elements is exactly the cell where the element should be if the array was sorted. We further show that we can sort in expected time Θ(n2 log n) by always picking two random cells and swapping their contents if they are not ordered correctly.