We construct a graph on a planar point set that captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraneous edges.Expand

We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph, improving by an order of magnitude previously known bounds.Expand

Natarajan reduced the problem of designing a certain type of mechanical parts orienter to that of finding reset sequences for monotonic deterministic finite automata when all states are initially possible.Expand

We implement a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Loffler, and Strash, and analyze its performance on a large corpus of real-world graphs.Expand

The straight skeleton of a polygon is a variant of the medial axis introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate.Expand

We show that treewidth is bounded by a function of the diameter in a minor-closed family, if and only if some apex graph does not belong to the family.Expand