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Elicitation and verification of learning via experts (EVOLVE) for creating a theoretical framework for active shooter incidents
- Award ID(s):
- 2318559
- PAR ID:
- 10612083
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Developments in the Built Environment
- Volume:
- 21
- Issue:
- C
- ISSN:
- 2666-1659
- Page Range / eLocation ID:
- 100635
- 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
