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 - Funding Information:
The research at the University of Southern California was supported by the National Science Foundation (NSF) under grant numbers 1724392, 1409987, 1817189 and 1837779. The research was also supported by the United States-Israel Binational Science Foundation (BSF) under grant number 2017692.
Funding Information:
∗The research at the University of Southern California was supported by the National Science Foundation (NSF) under grant numbers 1724392, 1409987, 1817189 and 1837779. The research was also supported by the United States-Israel Binational Science Foundation (BSF) under grant number 2017692. Copyright ©c 2019, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
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 -