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

08/11/2022

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by   Gill Barequet, et al.

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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 + ε)-approximation schemes under translations with O(ε^-d n)-time for d dimensions and O(nlogε^-1 + ε^-2)-time for two dimensions, and we give an O(f^d-1ε^1-2dn)-time algorithm when also allowing for rotations, parameterized on f, which we define as the slimness of the point set.