Approximation algorithm for rearrangement distances considering repeated genes and intergenic regions

Siqueira, Gabriel; Alexandrino, Alexsandro Oliveira; Oliveira, Andre Rodrigues; Dias, Zanoni

doi:10.1186/s13015-021-00200-w

Algorithms for Molecular Biology

Table 1 Summary of results for rearrangement problems

From: Approximation algorithm for rearrangement distances considering repeated genes and intergenic regions

Problem	Rearrangement model	Genome representation	Complexity	Best known approximation factor
Sorting Permutations by Transpositions	Transpositions	Permutation	NP-hard [11]	1.375 [12]
Sorting Permutations by Reversals	Reversals	Permutation	NP-hard [13]	1.375 [14]
Sorting Signed Permutations by Reversals	Reversals	Signed permutation	P [15]	–
Sorting Permutations by Reversals and Transpositions	Reversals and transpositions	Permutation	NP-hard [16]	\(2.8334 + \epsilon\) [17, 18]
Sorting Signed Permutations by Reversals and Transpositions	Reversals and transpositions	Signed permutation	NP-hard [16]	2 [19]
Transposition Distance on Strings	Transpositions	String	NP-hard	\(12k^a\) [20, 21]
Reversal Distance on Strings	Reversals	String	NP-hard	\(16k^a\) [20]
Signed Reversal Distance on Strings	Reversals	Signed string	NP-hard [22]	\(16k^a\) [7, 20]
Sorting Permutations by Intergenic Transpositions	Transpositions	Permutation and sequence of integers	NP-hard [23]	3.5 [23]
Sorting Permutations by Intergenic Reversals	Reversals	Permutation and sequence of integers	NP-hard [24]	4 [24]
Sorting Signed Permutations by Intergenic Reversals	Reversals	Signed permutation and sequence of integers	NP-hard [16]	2 [16]
Sorting Permutations by Intergenic Reversals and Transpositions	Reversals and transpositions	Permutation and sequence of integers	NP-hard [24]	4.5 [24]
Sorting Signed Permutations by Intergenic Reversals and Transpositions	Reversals and transpositions	Signed permutation and sequence of integers	NP-hard [25]	3 [25]
Intergenic Reversal Distance on Strings	Reversals	String and sequence of integers	NP-hard (Theorem 1)	\(6k^{a,b}\) (Corollary 2)
Intergenic Transposition Distance on Strings	Transposition	String and sequence of integers	NP-hard (Theorem 1)	\(8k^a\) (Corollary 4)
Intergenic Reversal and Transposition Distance on Strings	Reversal and transposition	String and sequence of integers	NP-hard (Theorem 1)	\(9k^a\) (Corollary 5)

\({}^a\)Some approximations depend on k, which is the maximum number of copies of a character in the string.
\({}^b\)Asymptotic approximation

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ISSN: 1748-7188

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