Reference Work Entry

Encyclopedia of Algorithms

pp 2026-2028


Sorting Signed Permutations by Reversal (Reversal Distance)

  • David A. BaderAffiliated withCollege of Computing, Georgia Institute of Technology Email author 


Inversion distance Reversal distance Sorting by reversals

Years and Authors of Summarized Original Work

  • 2001; Bader, Moret, Yan

Problem Definition

This entry describes algorithms for finding the minimum number of steps needed to sort a signed permutation (also known as inversion distance, reversal distance). This is a real-world problem and, for example, is used in computational biology.

Inversion distance is a difficult computational problem that has been studied intensively in recent years [1, 4, 610]. Finding the inversion distance between unsigned permutations is NP-hard [7], but with signed ones, it can be done in linear time [1].

Key Results

Bader et al. [1] present the first worst-case linear-time algorithm for computing the reversal distance that is simple and practical and runs faster than previous methods. Their key innovation is a new technique to compute connected components of the overlap graph using only a stack, which results in the simple linear-time algorithm for computing the inversion distance between two signed permutations. Ba ...

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