Computing Shortest Paths amid Convex Pseudodisks

Chen, Danny Z.; Hershberger, John; Wang, Haitao

doi:10.1137/110840030

Cited by 11 publications

(9 citation statements)

References 20 publications

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“…Their algorithm is similar to shortest path finding in a simple polygon but uses a trapezoid decomposition in place of polygon triangulation. For finding shortest paths among curved obstacles (the splinegon version of a polygonal domain) there is recent work [10], and also more efficient algorithms when the curves are more specialized [9,21].…”

Section: Related Workmentioning

confidence: 99%

Visibility graphs, dismantlability, and the cops and robbers game

Lubiw¹,

Snoeyink²,

Vosoughpour³

2017

Computational Geometry

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We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs are dismantlable, which is interesting as one of the few results relating visibility graphs to other known graph classes. We extend this to show that the cop wins games in which players move along straight line segments inside any polygon and, more generally, inside any simply connected planar region with a reasonable boundary. Essentially, our problem is a type of pursuit-evasion using the link metric rather than the Euclidean metric, and our result provides an interesting class of infinite cop-win graphs.

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Section: Related Workmentioning

confidence: 99%

Visibility graphs, dismantlability, and the cops and robbers game

Lubiw¹,

Snoeyink²,

Vosoughpour³

2017

Computational Geometry

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“…If the query points s and t are both restricted to the boundaries of the obstacles of P, Bae and Okamato [1] built a data structure of size O(n 5 poly(log n)) that answers each query in O(log n) time, where poly(log n) is a polylogarithmic factor. Efficient algorithms were also given for the case when the obstacles have curved boundaries [5,10,13,22,25].…”

Section: Related Workmentioning

confidence: 99%

Two-Point L1 Shortest Path Queries in the Plane

Chen

Inkulu

Wang

2014

Proceedings of the Thirtieth Annual Symposium on Computational Geometry

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Let P be a set of h pairwise-disjoint polygonal obstacles with a total of n vertices in the plane. In this paper, we consider the problem of building a data structure that can quickly compute an L1 shortest obstacle-avoiding path between any two query points s and t. We build a data structure of sizewhere k is the number of edges of the output path. Note that n+h 2 ·log 2 h· 4 √ log h = O(n+h 2+ϵ ) for any constant ϵ > 0. We also extend our techniques to the weighted rectilinear version in which the "obstacles" of P are rectilinear regions with "weights" and allow L1 paths to travel through them with weighted costs. Our algorithm answers each query in O(log n + k) time with a data structure of size O(n 2 · log n · 4 √ log n ) that is built in O(n 2 · log 2 n · 4 √ log n ) time.

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“…Hershberger et al [6] propose an algorithm for the problem of computing shortest paths among curved obstacles in the plane. Chen et al [7] shown technique which is also applicable to a motion planning problem of finding a short-est path to translate a convex object in the plane from one location to another avoiding a given set of polygonal obstacles, improving the previously best known solution and settling an open problem posed in 1988. Chen et al [8] study the problem of computing an L1 (or rectilinear) shortest path between two points avoiding the obstacles.…”

Section: Related Workmentioning

confidence: 99%