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Sorting circular permutations by bounded transpositions.

Xuerong Feng¹, Bhadrachalam Chitturi, Hal Sudborough

¹Department of Biochemistry, University of Texas SW Medical Center, Dallas, TX 75390, USA.

Advances in Experimental Medicine and Biology

|September 25, 2010

Summary

This summary is machine-generated.

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Sorting algorithms using adjacent swaps and short swaps are analyzed. Adjacent swaps have a lower bound of (1/4)n^2, while short swaps achieve upper bounds of (5/32)n^2 for sequential and (7/8)n for parallel sorting.

Area of Science:

Computational biology
Discrete mathematics
Algorithm analysis

Background:

Transpositions are operations that switch elements with a bounded distance.
k-bounded transpositions are relevant to gene order rearrangements in biological systems.
Sorting circular permutations is a fundamental problem in computer science.

Purpose of the Study:

To analyze sorting algorithms using k-bounded transpositions, specifically for k=2 (adjacent swaps) and k=3 (short swaps).
To establish theoretical bounds for sorting efficiency under these operations.
To model gene order microrearrangements in biological contexts.

Main Methods:

Proving a lower bound for sorting using adjacent swaps.
Deriving upper bounds for sequential and parallel sorting using short swaps.

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Analyzing the computational complexity of these sorting operations.

Main Results:

A lower bound of (1/4)n^2 is proven for sorting by adjacent swaps.
An upper bound of (5/32)n^2 + O(n log n) is established for sequential sorting by short swaps.
An upper bound of (7/8)n + O(log n) is shown for parallel sorting by short swaps.

Conclusions:

Adjacent swaps have a quadratic lower bound for sorting.
Short swaps offer more efficient sorting, with distinct bounds for sequential and parallel processing.
The study provides insights into the computational complexity of gene order rearrangements.