Competitive Searching in a Generalized Street

We consider the problem of a robot which has to find a target in an unknown simple polygon, based only on what it has seen so far. A street is a polygon for which the two boundary chains from start to target are mutually weakly visible. A target inside a street can be found by walking a path that is at most a constant times longer than the shortest path in the street from start to target. We define a strictly larger class of polygons, called generalized streets or G-streets, which are characterized by the property that every point on the boundary of a G-street is visible from a point on a horizontal line segment connecting the two boundary chains. We present an on-line strategy for a robot to find the target in an unknown rectilinear G-street; the length of its path is at most 9 times the length of the shortest path in the L1 metric, and 9.06 times the length of the L2-shortest path. These bounds are optimal. Key words: Simple polygon, street, searching, doubling, competitive.

• Type: Conference
• Year: 1994
• Where: COMPGEOM
• Authors: Amitava Datta, Christian Icking
• Keywords: Boundary Chains, COMPGEOM 1994, Discrete Geometry, Shortest Path, Unknown Simple Polygon