We examine the existence of tangent hyperplanes to subriemannian balls. Strictly abnormal shortest paths are allowed.

We consider two approaches that model timetable information in public transportation systems as shortestpath problems in weighted graphs. In the time-expanded approach every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the time-dependent approach the graph contains only one node per station. Both approaches have been recently considered for the...

Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called “Wiener” polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called “thorny” graph are considered and shown to be related to the weighted and unweighted q...

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the ...

We introduce a path-based measure of convexity to be used in assessing the compactness of legislative districts. Our measure is the probability that a district will contain the shortest path between a randomly selected pair of its’ points. The measure is defined relative to exogenous political boundaries and population distributions. JEL classification: D72, K00, K19

Message routing strategies are given for any network that can be decomposed by a separator of size at most a small constant c into two networks with the same property. These strategies use a total of O(cnlogn) items of routing information, keep node names to O(log n) bits, and still route along near-shortest paths. If the names generated from a separator-based hierarchical decomposition of the ...

The problem of determining shortest paths in the presence of polyhedral obstacles between two points in Euclidean 3-space stems from the general problem of obtaining optimal coliision free paths in robot systems. For the special case when paths are constrained to the surfaces of 3-dimensional objects, simple planar unfoldings are used to obtain the shortest path. For the general case wben paths...

In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them featuring the cutpoint additive distances. These include the path distances, the reliability distance, the walk distances, and the logarithmic forest distances among...