Art gallery theorems and algorithms
Art gallery theorems and algorithms
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Characterizing LR-visibility polygons and related problems
Computational Geometry: Theory and Applications
Finding all weakly-visible chords of a polygon in linear time
Nordic Journal of Computing
Triangulating a simple polygon in linear time
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Optimization Algorithms for Sweeping a Polygonal Region with Mobile Guards
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Optimum sweeps of simple polygons with two guards
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
An optimal algorithm for the 1-searchability of polygonal rooms
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
The two-guard problem revisited and its generalization
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Minimization of the maximum distance between the two guards patrolling a polygonal region
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Optimum sweeps of simple polygons with two guards
Information Processing Letters
Characterizing and recognizing LR-visibility polygons
Discrete Applied Mathematics
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A polygon P admits a walk from a boundary point s to another boundary point t if two guards can simultaneously walk along the two boundary chains of P from s to t such that they are always visible to each other. A walk is called a straight walk if no backtracking is required during the walk. A straight walk is discrete if only one guard is allowed to move at a time, while the other guard waits at a vertex. We present simple, optimal O(n) time algorithms to determine all pairs of points of P which admit walks, straight walks and discrete straight walks. The chief merits of the algorithms are that these require simple data structures and do not assume a triangulation of P. Furthermore, the previous algorithms for the straight walk and the discrete straight walk versions ran in O(n log n) time even after assuming a triangulation.