The FastMap Algorithm for Shortest Path Computations

06/08/2017
by   Liron Cohen, et al.
0

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. In this space, the Euclidean distance between any two nodes 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 using A* search with the Euclidean distances as heuristic estimates. Our preprocessing algorithm, dubbed 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. Our FastMap algorithm also produces admissible and consistent heuristics and therefore guarantees the generation of optimal paths. Moreover, FastMap works on general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not always well defined. Empirically too, we demonstrate that the FastMap heuristic is competitive with other state-of-the-art heuristics like the Differential heuristic.

READ FULL TEXT

page 5

page 6

research
08/06/2023

A fast algorithm for All-Pairs-Shortest-Paths suitable for neural networks

Given a directed graph of nodes and edges connecting them, a common prob...
research
02/24/2021

A New Algorithm for Euclidean Shortest Paths in the Plane

Given a set of pairwise disjoint polygonal obstacles in the plane, findi...
research
12/07/2022

Learning Graph Search Heuristics

Searching for a path between two nodes in a graph is one of the most wel...
research
12/22/2022

TransPath: Learning Heuristics For Grid-Based Pathfinding via Transformers

Heuristic search algorithms, e.g. A*, are the commonly used tools for pa...
research
05/30/2019

Power Weighted Shortest Paths for Unsupervised Learning

We study the use of power weighted shortest path distance functions for ...
research
12/12/2014

Manifold Matching using Shortest-Path Distance and Joint Neighborhood Selection

Matching datasets of multiple modalities has become an important task in...
research
11/19/2021

Embeddings and labeling schemes for A*

A* is a classic and popular method for graphs search and path finding. I...

Please sign up or login with your details

Forgot password? Click here to reset