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arXiv · 1703.06983

Collapsibility to a subcomplex of a given dimension is NP-complete

Giovanni Paolini
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Abstract

In this paper we extend the works of Tancer and of Malgouyres and Francés, showing that $(d,k)$-collapsibility is NP-complete for $d\geq k+2$ except $(2,0)$. By $(d,k)$-collapsibility we mean the following problem: determine whether a given $d$-dimensional simplicial complex can be collapsed to some $k$-dimensional subcomplex. The question of establishing the complexity status of $(d,k)$-collapsibility was asked by Tancer, who proved NP-completeness of $(d,0)$ and $(d,1)$-collapsibility (for $d\geq 3$). Our extended result, together with the known polynomial-time algorithms for $(2,0)$ and $d=k+1$, answers the question completely.

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Giovanni Paolini. 2019-04-05. Collapsibility to a subcomplex of a given dimension is NP-complete. https://doi.org/10.1007/s00454-017-9915-6

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