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A process inspired by fractals for embedding digital codes into additively manufactured components for supply chain security
- Award ID(s):
- 1946231
- PAR ID:
- 10568047
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 15
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Beyersdorff, Olaf; Kanté, Mamadou Moustapha; Kupferman, Orna; Lokshtanov, Daniel (Ed.)Given a set P of n points and a set S of n segments in the plane, we consider the problem of computing for each segment of S its closest point in P. The previously best algorithm solves the problem in n^{4/3}2^{O(log^*n)} time [Bespamyatnikh, 2003] and a lower bound (under a somewhat restricted model) Ω(n^{4/3}) has also been proved. In this paper, we present an O(n^{4/3}) time algorithm and thus solve the problem optimally (under the restricted model). In addition, we also present data structures for solving the online version of the problem, i.e., given a query segment (or a line as a special case), find its closest point in P. Our new results improve the previous work.more » « less
