TY - GEN
T1 - Using fastmap to solve graph problems in a euclidean space
AU - Li, Jiaoyang
AU - Felner, Ariel
AU - Koenig, Sven
AU - Satish Kumar, T. K.
N1 - Publisher Copyright:
© 2019, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - It is well known that many graph problems, like the Traveling Salesman Problem, are easier to solve in a Euclidean space. This motivates the idea of quickly preprocessing a given graph by embedding it in a Euclidean space to solve graph problems efficiently. In this paper, we study a nearlinear time algorithm, called FastMap, that embeds a given non-negative edge-weighted undirected graph in a Euclidean space and approximately preserves the pairwise shortest path distances between vertices. The Euclidean space can then be used either for heuristic guidance of A∗ (as suggested previously) or for geometric interpretations that facilitate the application of techniques from analytical geometry. We present a new variant of FastMap and compare it with the original variant theoretically and empirically. We demonstrate its usefulness for solving a path-finding and a multi-agent meeting problem.
AB - It is well known that many graph problems, like the Traveling Salesman Problem, are easier to solve in a Euclidean space. This motivates the idea of quickly preprocessing a given graph by embedding it in a Euclidean space to solve graph problems efficiently. In this paper, we study a nearlinear time algorithm, called FastMap, that embeds a given non-negative edge-weighted undirected graph in a Euclidean space and approximately preserves the pairwise shortest path distances between vertices. The Euclidean space can then be used either for heuristic guidance of A∗ (as suggested previously) or for geometric interpretations that facilitate the application of techniques from analytical geometry. We present a new variant of FastMap and compare it with the original variant theoretically and empirically. We demonstrate its usefulness for solving a path-finding and a multi-agent meeting problem.
UR - http://www.scopus.com/inward/record.url?scp=85085601106&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85085601106
T3 - Proceedings International Conference on Automated Planning and Scheduling, ICAPS
SP - 273
EP - 278
BT - Proceedings of the 29th International Conference on Automated Planning and Scheduling, ICAPS 2019
A2 - Benton, J.
A2 - Lipovetzky, Nir
A2 - Onaindia, Eva
A2 - Smith, David E.
A2 - Srivastava, Siddharth
PB - AAAI press
T2 - 29th International Conference on Automated Planning and Scheduling, ICAPS 2019
Y2 - 11 July 2019 through 15 July 2019
ER -