Given a polygonal curve and a geometric graph, we describe an efficient algorithm to find a path in the graph which is most similar to the curve, using the well-known Fréchet distance for curves.

We present an O(nlog/sup 1+/spl epsiv// n)-time algorithm for computing the optimal robot motion that maintains line-of-sight visibility between a target moving inside a polygon with n vertices which may contain holes. The motion is optimal for the tracking robot (the observer) in the sense that the target either remains visible for the longest possible time, or it is captured by the observer in the minimum time when feasible. Thus, the algorithm maximizes the minimum time-to-escape. Our algorithm assumes that the target moves along a known path. Thus, it is an off-line algorithm. Our theoretical results for the algorithm's runtime assume that the target is moving along a shortest path from its source to its destination. This assumption, however is not required to prove the optimality of the computed solution, hence the algorithm remains correct for the general case.