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Index Terms
- Navigating in unfamiliar geometric terrain
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Reviews
Kirk Pruhs
The setting for the problems considered in this paper is a plane littered with obstacles and inhabited by a robot. The locations and shapes of the obstacles are initially unknown to the robot. The robot's goal is to find a short, obstacle-avoiding path to some predetermined location. The authors use competitive analysis to compare different possible algorithms for this problem. The problem was introduced by Papadimitriou and Yanakakis [1], who gave an optimally competitive algorithm for objects of bounded aspect ratio. In this paper the authors consider the case in which the obstacles are oriented rectangles. They break the general problem down into two subproblems, the room problem and the wall problem. In the wall problem the robot's goal is to move to some location on an infinite line, and in the room problem the robot's goal is to move to some point on a rectangle enclosing the scene. The authors present an algorithm with a competitive factor of O 2 c log n for the room problem, where n is the length of the shortest obstacle-avoiding path. They also give an algorithm with a competitive factor of O n for the wall problem; this yields an algorithm with the same competitive factor for the general problem with oriented rectangles. The paper is quite readable. The authors pose many interesting open problems, such as determining the optimal competitive factor for the room problem. On the negative side, due to the high competitive factors involved, it is not clear how useful the algorithms would be in practice.
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