We consider the point-to-point (approximate) shortest-path query problem, which is the
following generalization of the classical single-source (SSSP) and all-pairs shortest-path …

The shortest path problem is a fundamental problem with numerous applications. In this
paper we study one of the most common variants of the problem, where the goal is to find a …

A shortest-path algorithm finds a path containing the minimal cost between two vertices in a
graph. A plethora of shortest-path algorithms is studied in the literature that span across …

We present a route planning technique solely based on the concept of node contraction. The
nodes are first ordered by 'importance'. A hierarchy is then generated by iteratively …

Algorithms for route planning in transportation networks have recently undergone a rapid
development, leading to methods that are up to three million times faster than Dijkstra's …

Algorithms are at the heart of every nontrivial computer application, and algorithmics is a
modern and active area of computer science. Every computer scientist and every …

We present a new speedup technique for route planning that exploits the hierarchy inherent
in real world road networks. Our algorithm preprocesses the eight digit number of nodes …

We study novel combinatorial properties of graphs that allow us to devise a completely new
approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic …

In the single-source shortest paths problem, the goal is to compute the shortest path tree
from a designated source vertex in a weighted, directed graph. We present the first near …

Although there are many advanced and specialized texts and handbooks on algorithms,
until now there was no book that focused exclusively on the wide variety of data structures …