Abstract
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.
Highlights
In geographical context, network analysis is a type of geographical analysis on real world networks, such as road, subway, or river networks
The objective is to determine the dilation of typical polygons one can expect in practice when using 1, 2, or more feed-links, and to compare which feed-link placement heuristic gives the best resulting dilation
We studied the problem of extending a partial road network by adding feed-links to relevant disconnected locations
Summary
Network analysis is a type of geographical analysis on real world networks, such as road, subway, or river networks. One may analyze how many households are reachable within 45 minutes from a fire station In this case, the households are typically aggregated by municipality or postal-code region, and the centroid of this region is taken as the representative point. The households are typically aggregated by municipality or postal-code region, and the centroid of this region is taken as the representative point It might even be far removed from it, since nationwide accessibility studies rarely use detailed network data for their analysis. National or provincial authorities are often responsible only for roads of a certain level and do not record local or smaller roads in their databases
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