dc.citation.conferencePlace |
US |
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dc.citation.conferencePlace |
New Orleans |
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dc.citation.endPage |
774 |
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dc.citation.startPage |
766 |
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dc.citation.title |
18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 |
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dc.contributor.author |
Cheng, Siu-Wing |
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dc.contributor.author |
Na, Hyeon-Suk |
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dc.contributor.author |
Vigneron, Antoine |
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dc.contributor.author |
Wang, Yajun |
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dc.date.accessioned |
2023-12-20T05:06:52Z |
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dc.date.available |
2023-12-20T05:06:52Z |
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dc.date.created |
2016-07-04 |
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dc.date.issued |
2007-01-07 |
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dc.description.abstract |
Our goal is to find an approximate shortest path for a point robot moving in a planar subdivision with n vertices. Let ρ ≥ 1 be a real number. Distances in each face of this subdivision are measured by a convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean disk with radius 1/ρ. Different convex distance functions may be used for different faces, and obstacles are allowed. These convex distance functions may be asymmetric. For all ϵ ∈ (0, 1), and for any two points vs and vd, we give an algorithm that finds a path from vs to vd whose cost is at most (1 + ϵ) times the minimum cost. Our algorithm runs in O(ρ2 log ρ/ϵ2 n3 log (ρn/ϵ)) time. This bound does not depend on any other parameters; in particular, it does not depend on the minimum angle in the subdivision. We give applications to two special cases that have been considered before: the weighted region problem and motion planning in the presence of uniform flows. For the weighted region problem with weights in [1, ρ]∪{∞}, the time bound of our algorithm improves to O (ρ log ρ/ϵ n3 log (ρn ϵ)). Copyright © 2007 by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics. |
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dc.identifier.bibliographicCitation |
18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, pp.766 - 774 |
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dc.identifier.scopusid |
2-s2.0-84969233367 |
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dc.identifier.uri |
https://scholarworks.unist.ac.kr/handle/201301/34482 |
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dc.identifier.url |
http://dl.acm.org/citation.cfm?id=1283465&CFID=639749174&CFTOKEN=76434841 |
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dc.language |
영어 |
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dc.publisher |
18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 |
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dc.title |
Approximate shortest paths in anisotropic regions |
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dc.type |
Conference Paper |
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dc.date.conferenceDate |
2007-01-07 |
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