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

TL;DR

This paper presents a parallel algorithm for shortest-path queries in planar graphs, optimized for GPU-accelerated multi-node clusters, achieving efficient query times with distributed data structures.

Contribution

It introduces a divide-and-conquer parallel algorithm and a distributed data structure for fast shortest-path queries on planar graphs on GPU clusters.

Findings

Query time is $O(n^{1/4})$ per query.

Data structure requires $O(n)$ storage per processor.

Algorithm is efficient for large-scale planar graphs.

Abstract

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.