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

We develop an efficient parallel algorithm for answering shortest-path 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 vertices. For a planar graph with n vertices, that data structure needs O(n) storage per processor and allows queries to be answered in O(n(1/4)) time.