Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Shortest watchman routes in simple polygons
Discrete & Computational Geometry
Watchman routes under limited visibility
Computational Geometry: Theory and Applications
Information Sciences: an International Journal
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Developing algorithms and software for geometric path planning problems
ACM Computing Surveys (CSUR) - Special issue: position statements on strategic directions in computing research
Approximation algorithms for TSP with neighborhoods in the plane
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A new representation for linear lists
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Finding shortest safari routes in simple polygons
Information Processing Letters
Approximation algorithms for the watchman route and zookeeper's problems
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Shortest paths in simple polygons with polygon-meet constraints
Information Processing Letters
A fast approximation algorithm for TSP with neighborhoods and red-blue separation
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Hi-index | 5.23 |
In this paper, we study the problem of finding the shortest path between two points inside a simple polygon such that there is at least one point on the path from which a query point is visible. We provide an algorithm which preprocesses the input in O(n^2+nK) time and space and provides logarithmic query time. The input polygon has n vertices and K is a parameter dependent on the input polygon which is O(n^2) in the worst case but is much smaller for most polygons. The preprocessing algorithm sweeps an angular interval around every reflex vertex of the polygon to store the optimal contact points between the shortest paths and the windows separating the visibility polygons of the query points from the source and the destination.