Online exploration of all vertices in a simple polygon

Authors:
Yuya Higashikawa;Naoki Katoh
Affiliations:
Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo-ku, Kyoto, Japan;Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo-ku, Kyoto, Japan
Venue:
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
Year:
2012

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Abstract

This paper considers an online exploration problem in a simple polygon where starting from a point in the interior of a simple polygon, the searcher is required to explore a simple polygon to visit all its vertices and finally return to the initial position as quickly as possible. The information of the polygon is given online. As the exploration proceeds, the searcher gains more information of the polygon. We give a 1.219-competitive algorithm for this problem. We also study the case of a rectilinear simple polygon, and give a 1.167-competitive algorithm.