Road network analysis can require distance from points that are not on the network themselves. We study the algorithmic problem of connecting a point inside a face (region) of the road network to its boundary while minimizing the detour factor of that point to any point on the boundary of the face. We show that the optimal single connection (feed-link) can be computed in O(lambda_7(n) log n) time where n is the number of vertices that bounds the face and lambda_7(n) is the slightly superlinear maximum length of a Davenport-Schinzel sequence of order 7 on n symbols. We also present approximation results for placing more feed-links deal with the case that there are obstacles in the face of the road network that contains the point to be connected and present various related results.

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Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.