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arXiv · 2208.05597

Diamonds are Forever in the Blockchain: Geometric Polyhedral Point-Set Pattern Matching

Gill Barequet·Shion Fukuzawa·Michael T. Goodrich·David M. Mount·Martha C. Osegueda·Evrim Ozel
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Abstract

Motivated by blockchain technology for supply-chain tracing of ethically sourced diamonds, we study geometric polyhedral point-set pattern matching as minimum-width polyhedral annulus problems under translations and rotations. We provide two $(1 + \varepsilon)$-approximation schemes under translations with $O(\varepsilon^{-d} n)$-time for $d$ dimensions and $O(n\log \varepsilon^{-1} + \varepsilon^{-2})$-time for two dimensions, and we give an $O(f^{d-1}\varepsilon^{1-2d}n)$-time algorithm when also allowing for rotations, parameterized on $f$, which we define as the slimness of the point set.

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Gill Barequet, Shion Fukuzawa, Michael T. Goodrich, David M. Mount, Martha C. Osegueda, Evrim Ozel. 2022-08-11. Diamonds are Forever in the Blockchain: Geometric Polyhedral Point-Set Pattern Matching. https://arxiv.org/abs/2208.05597

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