COCOON 2004: Computing and Combinatorics pp 33-42

# Towards Constructing Optimal Strip Move Sequences

• Meena Mahajan
• Raghavan Rama
• S. Vijayakumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3106)

## Abstract

The Sorting by Strip Moves problem, SBSM, was introduced in [6] as a variant of the well-known Sorting by Transpositions problem. A restriction called Block Sorting was shown in [2] to be NP-hard. In this article, we improve upon the ideas used in [6] 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.

## Keywords

Single Edge Identity Permutation Order Graph Single Strip Inclusion Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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