The FastMap Algorithm for Shortest Path Computations

@article{Cohen2018TheFA,
  title={The FastMap Algorithm for Shortest Path Computations},
  author={Liron Cohen and Tansel Uras and Shiva Jahangiri and Aliyah Arunasalam and Sven Koenig and T. K. Satish Kumar},
  journal={ArXiv},
  year={2018},
  volume={abs/1706.02792}
}
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… 

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References

SHOWING 1-10 OF 49 REFERENCES
Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks
TLDR
CHs can be combined with many other route planning techniques, leading to improved performance for many-to-many routing, transit-node routing, goal-directed routing or mobile and dynamic scenarios, and a hierarchical query algorithm using bidirectional shortest-path search is obtained.
Near Optimal Hierarchical Path-Finding
TLDR
HPA* (Hierarchical Path-Finding A*), a hierarchical approach for reducing problem complexity in path-finding on grid-based maps, which abstracts a map into linked local clusters and works very well in domains with a dynamically changing environment.
Compressing Optimal Paths with Run Length Encoding
TLDR
A novel approach to Compressed Path Databases, space efficient oracles used to very quickly identify the first edge on a shortest path, being significantly faster than state-of-the-art first-move oracles from the literature is introduced.
Identifying Hierarchies for Fast Optimal Search
TLDR
This paper generalizes the partitioning process to any undirected graph and shows that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further.
A note on two problems in connexion with graphs
  • E. Dijkstra
  • Mathematics, Computer Science
    Numerische Mathematik
  • 1959
TLDR
A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
FastMap: a fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets
TLDR
A fast algorithm to map objects into points in some k-dimensional space (k is user-defined), such that the dis-similarities are preserved, and this method is introduced from pattern recognition, namely, Multi-Dimensional Scaling (MDS).
Optimizations of data structures, heuristics and algorithms for path-finding on maps
  • T. Cazenave
  • Computer Science
    2006 IEEE Symposium on Computational Intelligence and Games
  • 2006
TLDR
The best optimal pathfinder can be up to seven times faster than the commonly used pathfinders as shown by experimental results and some optimizations of A and IDA* for pathfinding on maps are presented.
A Formal Basis for the Heuristic Determination of Minimum Cost Paths
TLDR
How heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching is described and an optimality property of a class of search strategies is demonstrated.
Contraction Hierarchies on Grid Graphs
TLDR
This paper shows that contraction hierarchies can be applied to grid graphs as well, and points out interesting connections to speed-up techniques shaped for routing on grids, like swamp hierarchies and jump points, and provides experimental results for game maps, mazes, random grids and rooms.
Path Planning with Compressed All-Pairs Shortest Paths Data
TLDR
Part of the ideas have been integrated in the Copa CPD system, one of the two best optimal participants in the grid-based path planning competition GPPC.
...
...