The searching for the shortest path in public transport networks can take more time than is acceptable for given situation. We have therefore searched for methods that speed up the given calculation. The approach, when the calculation is not performed on the original network but on the simplified one, seems to be very promising. The path found in the simplified network can be easily mapped to a...

This paper presents a simple O(n + k) time algorithm to compute the set of k non-crossing shortest paths between k source-destination pairs of points on the boundary of a simple polygon of n vertices. Paths are allowed to overlap but are not allowed to cross in the plane. A byproduct of this result is an O(n) time algorithm to compute a balanced geodesic triangulation which is easy to implement...

All except one of these routes will mark detours, i.e. not the shortest connection between origin and destination. The proposed assignment method is intended to work with common operational models of pedestrian dynamics. These – as mentioned before – usually send pedestrians into the direction of the spatially shortest path. Thus, all detouring routes have to be equipped with intermediate desti...

Consider the curve C = {(t, f(t): 0 < t < 1}, where f is absolutely continuous on [0, 1]. Then C has finite length, and if Ue is the &neighborhood of f in the uniform norm, we compare the length of the shortest path in UE with the length of f. Our main result establishes necessary and sufficient conditions on f such that the difference of these quantities is of order e as e -* 0. We also includ...

Article history: Available online 10 April 2013