# Generalized streets revisited

## Abstract

We consider the problem of a robot inside an unknown polygon that has to find a path from a starting point *s* to a target point *t*. We assume that it is equipped with an on-board vision system through which it can get the visibility map of its surroundings. Furthermore, we assume that the robot is contained in a simple polygon that belongs to the class of polygons called generalized streets. We consider three problems.

- 1.
We present a strategy that allows the robot to search for

*t*in an arbitrarily oriented generalized street where the distance travelled by the robot under our strategy is at most 80 times the length of the shortest path from*s*to*t*. - 2.
We show that there are orthogonal generalized streets for which the distance travelled by the robot under any searching strategy is at least 9.06 times the length of the shortest path from

*s*to*t*. - 3.
Finally, we show that even if the location of the target is known, there are orthogonal generalized streets for which the distance travelled by the robot under any searching strategy is at least 9 times the length of the shortest path from

*s*to*t*.

## Keywords

Short Path Competitive Ratio Simple Polygon Robot Position Polygonal Chain## Preview

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