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arXiv · 2511.00015

Sorting by Strip Swaps is NP-Hard

Swapnoneel Roy·Asai Asaithambi·Debajyoti Mukhopadhyay
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Abstract

We show that \emph{Sorting by Strip Swaps} (SbSS) is NP-hard by a polynomial reduction of \emph{Block Sorting}. The key idea is a local gadget, a \emph{cage}, that replaces every decreasing adjacency $(a_i,a_{i+1})$ by a guarded triple $a_i,m_i,a_{i+1}$ enclosed by guards $L_i,U_i$, so the only decreasing adjacencies are the two inside the cage. Small \emph{hinge} gadgets couple adjacent cages that share an element and enforce that a strip swap that removes exactly two adjacencies corresponds bijectively to a block move that removes exactly one decreasing adjacency in the source permutation. This yields a clean equivalence between exact SbSS schedules and perfect block schedules, establishing NP-hardness.

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Swapnoneel Roy, Asai Asaithambi, Debajyoti Mukhopadhyay. 2025-10-20. Sorting by Strip Swaps is NP-Hard. https://arxiv.org/abs/2511.00015

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