Computing the visibility graph via pseudo-triangulations

Pocchiola, Michel; Vegter, Gert

doi:10.1145/220279.220306

Cited by 36 publications

(65 citation statements)

References 10 publications

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“…For a special case in which the n pseudodisks are all disks, the previously best algorithms compute a shortest path in O(n 2 log n) time [2,4], which is also the previously best result when all disks are pairwise disjoint; further, when all disks are of the same size, the algorithms in [8,19] can be applied to find a shortest path in visibility graphs is a fundamental research topic and has many applications (e.g., see [1,7,16,18,20]). For a set of pairwise disjoint polygons with a total of n vertices in the plane, O(n 2 )-time algorithms [1,20] and an O(K + n log n)-time output-sensitive algorithm [7] for computing the visibility graph were known, where K is the size of the visibility graph.…”

Section: Introductionmentioning

confidence: 72%

Computing Shortest Paths amid Convex Pseudodisks

Chen¹,

Hershberger²,

Wang³

2013

SIAM J. Comput.

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Multiple objects in the plane are called pseudodisks if the boundaries of any two of them intersect transversely at most twice. Given a set of n (possibly intersecting) convex pseudodisks of O(1) complexity each and two points s and t in the plane, we present an efficient algorithm for computing a shortest s-to-t path avoiding the pseudodisks. After the union of the pseudodisks is computed, which can be done in O(n log n) randomized time or O(n log 2 n) deterministic time, our algorithm runs in O(n log n + k) deterministic time, where k is the size of the extended visibility graph of the union of the pseudodisks. Note that k = O(n 2 ) in the worst case. In over two decades, the previously best algorithms for this problem have not improved on the bound of O(n 2 log n) time, even when all the pseudodisks are pairwise disjoint disks. Our technique is also applicable to a motion planning problem of finding a shortest 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. Our algorithm actually solves a more general version of the open problem. Further, as a byproduct of our approach, we present an O(n log n + k)-time algorithm for computing the extended visibility graph of a set of n (possibly intersecting) convex pseudodisks in the plane. The previously best known time bound for this visibility problem is O(n 2 log n).

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Section: Introductionmentioning

confidence: 72%

Computing Shortest Paths amid Convex Pseudodisks

Chen¹,

Hershberger²,

Wang³

2013

SIAM J. Comput.

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“…In this article, we use the visibility graph [1,7,8] to translate time series data set into a complex network. Intuitively, time series is difficult to translate into a graph with nodes and edges.…”

Section: Visibility Graphmentioning

confidence: 99%

A Complex Network of Well Log based on Visibility Graph

Xiao¹,

Chen²,

Xiao³

2014

IJSIP

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In this paper, we applied the visibility graph algorithm to change the well log data into a complex network. The degree distribution of this complex network existed exponential distribution, which indicated the scale free property of our network. Compared the original curve with the corresponding degree and cluster coefficient, we found that the shape information of original well log has been inherited by the network. The hierarchical coefficient of the complex network is about 2, which indicates the hierarchical structure in the network. All the data show that it is feasible and significant to translate the well log data into a complex network.

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“…All work-space cells together form the region that P may move in to accomplish O's desired motion. Computing a shortest path [14] through this region then yields a shortest contact-preserving push plan.…”

Section: Theoremmentioning

confidence: 99%

Computing push plans for disk-shaped robots

Berg

Gerrits

2010

2010 IEEE International Conference on Robotics and Automation

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Suppose we want to move a passive object along a given path, among obstacles in the plane, by pushing it with an active robot. We present two algorithms to compute a push plan for the case that the obstacles are non-intersecting line segments, and the object and robot are disks. The first algorithm assumes that the robot must maintain contact with the object at all times, and produces a shortest path. There are also situations, however, where the robot has no choice but to let go of the object occasionally. Our second algorithm handles such cases, but no longer guarantees that the produced path is the shortest possible.

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Computing the visibility graph via pseudo-triangulations

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Cited by 36 publications

References 10 publications

Computing Shortest Paths amid Convex Pseudodisks

Computing Shortest Paths amid Convex Pseudodisks

A Complex Network of Well Log based on Visibility Graph

Computing push plans for disk-shaped robots

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