Efficient Fastest-Path Computations in Road Maps

TL;DR

This paper introduces a new heuristic for the A* algorithm that significantly improves fastest-path computations in large road networks by reducing the number of vertices explored, enabling faster route calculations.

Contribution

The authors propose a simple, effective heuristic based on graph separators, computed efficiently in preprocessing, which outperforms existing heuristics in speed and accuracy.

Findings

Heuristic reduces vertices explored by an order of magnitude.

Experimental results show improved efficiency over existing heuristics.

The method scales well to large road networks.

Abstract

In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are becoming a standard feature of many navigation-related applications. To support this, very efficient computation of these paths in very large road networks is critical. Fastest paths may be computed as minimal-cost paths in a weighted directed graph, but traditional minimal-cost path algorithms based on variants of the classic Dijkstra algorithm do not scale well, as in the worst case they may traverse the entire graph. A common improvement, which can dramatically reduce the number of traversed graph vertices, is the A* algorithm, which requires a good heuristic lower bound on the minimal cost. We introduce a simple, but very effective, heuristic function based on a small number of values assigned to each graph vertex. The values are based on graph separators and computed efficiently in a preprocessing stage. We present experimental results demonstrating that our heuristic provides estimates of the minimal cost which are superior to those of other heuristics. Our experiments show that when used in the A* algorithm, this heuristic can reduce the number of vertices traversed by an order of magnitude compared to other heuristics.