Computational geometry: an introduction
Computational geometry: an introduction
Navigating in unfamiliar geometric terrain
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Walking an unknown street with bounded detour
Computational Geometry: Theory and Applications
Information and Computation
Competitive searching in a generalized street
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Searching for the kernel of a polygon—a competitive strategy
Proceedings of the eleventh annual symposium on Computational geometry
New competitive strategies for searching in unknown star-shaped polygons
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tight analysis of a self-approaching strategy for the online kernel-search problem
Information Processing Letters
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Randomized robot navigation algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
On-line search in a simple polygon
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Algorithm for Finding the Kernel of a Polygon
Journal of the ACM (JACM)
Position-Independent Near Optimal Searching and On-line Recognition in Star Polygons
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
An optimal competitive strategy for walking in streets
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
An optimal strategy for searching in unknown streets
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Survey: Online algorithms for searching and exploration in the plane
Computer Science Review
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We study the problem of on-line searching for a target inside a polygon. In particular, we propose a strategy for finding a target of unknown location in a star-shaped polygon with a competitive ratio of 11.52. We also provide a lower bound of 9 for the competitive ratio of searching in a star-shaped polygon which is close to the upper bound. A similar task is the on-line recognition of a star-shaped polygon P. Here, the robot travels on a path that allows it to decide whether P is star-shaped or not. We present a strategy with a competitive ratio of 28.85 and give a lower bound of √82 for this problem.