Salvato in:
| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.10323 |
| Tags: |
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Sommario:
- Given a chain of $HW$ cubes where each cube is marked "turn $90^\circ$" or "go straight", when can it fold into a $1 \times H \times W$ rectangular box? We prove several variants of this (still) open problem NP-hard: (1) allowing some cubes to be wildcard (can turn or go straight); (2) allowing a larger box with empty spaces (simplifying a proof from CCCG 2022); (3) growing the box (and the number of cubes) to $2 \times H \times W$ (improving a prior 3D result from height $8$ to $2$); (4) with hexagonal prisms rather than cubes, each specified as going straight, turning $60^\circ$, or turning $120^\circ$; and (5) allowing the cubes to be encoded implicitly to compress exponentially large repetitions.