Using fastmap to solve graph problems in a euclidean space

Jiaoyang Li, Ariel Felner, Sven Koenig, T. K. Satish Kumar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

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 languageEnglish
Title of host publicationProceedings of the 29th International Conference on Automated Planning and Scheduling, ICAPS 2019
EditorsJ. Benton, Nir Lipovetzky, Eva Onaindia, David E. Smith, Siddharth Srivastava
PublisherAssociation for the Advancement of Artificial Intelligence
Pages273-278
Number of pages6
ISBN (Electronic)9781577358077
DOIs
StatePublished - 2019
Externally publishedYes
Event29th International Conference on Automated Planning and Scheduling, ICAPS 2019 - Berkeley, United States
Duration: 11 Jul 201915 Jul 2019

Publication series

NameProceedings International Conference on Automated Planning and Scheduling, ICAPS
ISSN (Print)2334-0835
ISSN (Electronic)2334-0843

Conference

Conference29th International Conference on Automated Planning and Scheduling, ICAPS 2019
Country/TerritoryUnited States
CityBerkeley
Period11/07/1915/07/19

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.

FundersFunder number
National Science Foundation1409987, 1724392, 1837779, 1817189
Bonfils-Stanton Foundation
Bloom's Syndrome Foundation2017692
United States-Israel Binational Science Foundation

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