# The FastMap Algorithm for Shortest Path Computations

# The FastMap Algorithm for Shortest Path Computations

## Liron Cohen, Tansel Uras, Shiva Jahangiri, Aliyah Arunasalam, Sven Koenig, T. K. Satish Kumar

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

Main track. Pages 1427-1433.
https://doi.org/10.24963/ijcai.2018/198

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with an A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data-mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic.

Keywords:

Heuristic Search and Game Playing: Heuristic Search

Heuristic Search and Game Playing: Combinatorial Search and Optimisation