Abstract
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.
Original language | English |
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Title of host publication | Proceedings of the 29th International Conference on Automated Planning and Scheduling, ICAPS 2019 |
Editors | J. Benton, Nir Lipovetzky, Eva Onaindia, David E. Smith, Siddharth Srivastava |
Publisher | Association for the Advancement of Artificial Intelligence |
Pages | 273-278 |
Number of pages | 6 |
ISBN (Electronic) | 9781577358077 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Event | 29th International Conference on Automated Planning and Scheduling, ICAPS 2019 - Berkeley, United States Duration: 11 Jul 2019 → 15 Jul 2019 |
Publication series
Name | Proceedings International Conference on Automated Planning and Scheduling, ICAPS |
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ISSN (Print) | 2334-0835 |
ISSN (Electronic) | 2334-0843 |
Conference
Conference | 29th International Conference on Automated Planning and Scheduling, ICAPS 2019 |
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Country/Territory | United States |
City | Berkeley |
Period | 11/07/19 → 15/07/19 |
Bibliographical note
Publisher Copyright:© 2019, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
Funding
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. ∗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.
Funders | Funder number |
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National Science Foundation | 1409987, 1724392, 1837779, 1817189 |
Bonfils-Stanton Foundation | |
Bloom's Syndrome Foundation | 2017692 |
United States-Israel Binational Science Foundation |