Towards Constructing Optimal Strip Move Sequences
The Sorting by Strip Moves problem, SBSM, was introduced in  as a variant of the well-known Sorting by Transpositions problem. A restriction called Block Sorting was shown in  to be NP-hard. In this article, we improve upon the ideas used in  to obtain a combinatorial characterization of the optimal solutions of SBSM. Using this, we show that a strip move which results in a permutation of two or three fewer strips or which exchanges a pair of adjacent strips to merge them into a single strip necessarily reduces the strip move distance. We also establish that the strip move diameter for permutations of size n is n–1. Further, we exhibit an optimum-preserving equivalence between SBSM and the Common Substring Removals problem (CSR) – a natural combinatorial puzzle. As a consequence, we show that sorting a permutation via strip moves is as hard (or as easy) as sorting its inverse.
KeywordsSingle Edge Identity Permutation Order Graph Single Strip Inclusion Graph
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