Shortest Beer Path Queries in Outerplanar Graphs

Shortest-Path Queries in Planar Graphs on GPU-Accelerated Architectures

We develop an efficient parallel algorithm for answering shortestpath queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small and roughly equal subgraphs and constructs a distributed data structure containing shortest distances within each of those subgraphs and between their boundary...

Exact Shortest Path Queries for Planar Graphs Using Linear Space

We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar graph G with non-negative arc lengths and for any > 0 there is a data structure that supports exact shortest path and distance queries in G with the following properties: the data structure can be created in time O(n lg(...

Shortest path queries in rectilinear worlds

Shortest Inspection-Path Queries in Simple Polygons

We want to preprocess a simple n-vertex polygon P to quickly determine the shortest path from a fixed source point s ∈ P to some point visible from a query point q ∈ P . We call such queries inspection-path queries. We give an algorithm that computes a data structure which answers the queries in logarithmic time. The data structure has O(n) size and can be computed in O(n logn) time.

Levelwise Mesh Sparsification for Shortest Path Queries

The shortest path problem is one of the most fundamental problems in computer science. Although several quasi linear time algorithms have been proposed, even an optimal algorithm does not terminate in sufficiently short time for large-scale networks, such as web networks and road networks. An approach to solving this problem is to construct data structures that enable us to find solutions in a ...