Computing the Visibility Polygon from a Convex Set and Related Problems

@article{Ghosh1991ComputingTV,
  title={Computing the Visibility Polygon from a Convex Set and Related Problems},
  author={Subir Kumar Ghosh},
  journal={J. Algorithms},
  year={1991},
  volume={12},
  pages={75-95}
}
  • S. Ghosh
  • Published 2 January 1991
  • Computer Science, Mathematics
  • J. Algorithms
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72 Citations
Highly Influential Citations
5
Background Citations
20
Methods Citations
15
Results Citations
1

72 Citations

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Maintaining the Visibility Graph of a Dynamic Simple Polygon

This algorithm preprocesses the initial simple polygon P to build few data structures, including the visibility graph of P, and is designed to compute the vertices of the current simplepolygon that are visible from a query point.

Optimal Shortest Path and Minimum-Link Path Queries Between Two Convex Polygons Inside a Simple Polygonal Obstacle

It is shown that shortest-path queries can be performed optimally in time O(logh + logn) (plus O(k) time for reporting the k edges of the path) using a data structure with O(n) space and preprocessing time, and that minimum-link- path queries can also be performed in optimal time.

Structured visibility profiles with applications to problems in simple polygons (extended abstract)

The structured visibility profile of a polygonal path is defined and how to compute it in linear time is shown and this result is applied to solve many problems inlinear time that previously required triangulation.

Parallel Algorithms for All Minimum Link Paths and Link Center Problems

This work shows that minimum link paths from a point to all vertices of P can be computed in O(log2n log log n) time using O(n) processors and proposes a parallel algorithm for computing the link center of P, which is the set of points x inside P such that the link distance from x to any other point in P is minimized.

Query-points visibility constraint minimum link paths in simple polygons

This work studies the query version of constrained minimum link paths between two points inside a simple polygon P with n vertices such that there is at least one point on the path, visible from a query point, and proposes an algorithm with O(n) preprocessing time.

Dynamic algorithms for visibility polygons

We devise the following dynamic algorithms for both maintaining as well as querying for the visibility and weak visibility polygons amid vertex insertions and/or deletions to the simple polygon. * A…

Minimum Link Fencing

A variant of the geometric multicut problem, where a set P of colored and pairwise interior-disjoint polygons in the plane is given, it is shown that BMLF is NP -hard in general and that it is XP -time solvable when each fence contains at most two polygons and the number of segments per fence is the parameter.
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References

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