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A Sensing Framework for Indoor Spatial Awareness for Blind and Visually Impaired Users
- Award ID(s):
- 1645737
- PAR ID:
- 10087024
- Publisher / Repository:
- Institute of Electrical and Electronics Engineers
- Date Published:
- Journal Name:
- IEEE Access
- Volume:
- 7
- ISSN:
- 2169-3536
- Page Range / eLocation ID:
- p. 10343-10352
- 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
