In the first part of the paper, we reexamine the all-pairs shortest paths (APSP) problem and present a new algorithm with running time O(n3 log3 log n/ log2 n), which improves all...
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n ...
David Eppstein, Michael T. Goodrich, Darren Strash
We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy...
Robert Geisberger, Moritz Kobitzsch, Peter Sanders
Abstract. A parametric weighted graph is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obta...
Sourav Chakraborty, Eldar Fischer, Oded Lachish, R...
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe an alg...