Feed-links for network extensions

Road network data is often incomplete, making it hard to perform network analysis. This paper discusses the problem of extending partial road networks with reasonable links, using the concept of dilation (also known as crow flight conversion coefficient). To this end, we study how to connect a point (relevant location) inside a polygon (face of the known part of the road network) to the boundary so that the dilation from that point to any point on the boundary is not too large. We provide algorithms and heuristics, and give a computational and experimental analysis

Computing Approximate Shortest Paths on Convex Polytopes

The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R³, two points s, t ∈ P, and a parameter ε > 0, it computes a path between s and t on P whose length is at most (1+ε) times the length of the shortest path between those points. It first constructs in time O(n/√ε) a graph of size O(1/ε^4), computes a shortest path on this graph, and projects the path onto the surface in O(n/ε) time, where n is the number of vertices of P. In the postprocessing step we have added a heuristic that considerably improves the quality of the resulting path