论文标题
钻石永远存在于区块链中：几何多面角点集匹配
Diamonds are Forever in the Blockchain: Geometric Polyhedral Point-Set Pattern Matching
论文作者
论文摘要
由区块链技术用于供应链的供应链的供应钻石的供应链，我们研究了几何多面角点集匹配，这是在翻译和旋转下的最小宽度多面环问题。我们提供两个$（1 + \ varepsilon）$ - 翻译下的近似方案，带有$ o（\ varepsilon^{ - d} n）$ - $ d $ dimensions和$ o的时间和$ o（n \ log \ log \ varepsilon^{ - 1} + \ varepsilon^{-2 $ O（f^{d-1} \ varepsilon^{1-2d} n）$ - 时间算法也允许旋转时，在$ f $上进行了参数化，我们将其定义为点集的纤细度。
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.
