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Table 1 Estimating Δτ. Changes of m(π), r(π), a(π), and τ (π) by applying the different sequences of operations described in this section. Case C' is the case where we cannot solve Case C directly and have to apply the sequence for Case A twice.l denotes the length of inserted or removed segments. Note that for all sequences, Δτ > 0.

From: Sorting by reversals, block interchanges, tandem duplications, and deletions

Sequence

Δm(π)

Δr(π)

Δa(π)

Δτ(π)

Inverse Tandem Duplication

0

-l

≥ -l

l

Segments with multiplicity ≥ 3

0

-2l

≥ -2l - 1

≥ 2l - 1

Creating adjacencies

0

0

≥ 1

≥ 1

Case A

-l

0

l

2l

Case B

0

-l

≥ -l

l

Case C

0

l

≥ -l

l

Case C'

-l

l

2l

2l