Advances in Spatial and Temporal Databases
Volume 2121 of the series Lecture Notes in Computer Science pp 217235
On MultiWay Spatial Joins with Direction Predicates
 Hongjun ZhuAffiliated withDepartment of Computer Science, University of California
 , Jianwen SuAffiliated withDepartment of Computer Science, University of California
 , Oscar H. IbarraAffiliated withDepartment of Computer Science, University of California
Abstract
Spatial joins are fundamental in spatial databases. Over the last decade, the primary focus of research has been on joins with the predicate “region intersection.” In modern database applications involving geospatial data such as GIS, efficient evaluation of joins with other spatial predicates is yet to be fully explored. In addition, most existing join algorithms were developed for twoway joins. Traditionally, a multiway join is treated as a sequence of twoway joins. The goal of this paper is to study evaluation of multiway spatial joins with direction predicates: complexity bounds and efficient algorithms. We first give I/O efficient plane sweeping based algorithms for 2way direction joins and show that by combining the plane sweeping technique with external priority search trees, a 2way direction join of Ntuple relations can be evaluated in O(Nlog_{b} N/M + k) I/Os in the worst case, where M is the size of the memory, b is the page size and k is the result size. The algorithms are then extended to perform a subclass of multiway direction joins called “star joins”. We show that the I/O complexity of evaluating an way star join of Ntuple relations is O(mN log_{b} MN +K + k), where mN ^{2} is the size of the intermediate result, M, b and k (= N ^{m}) are the same as above. We also apply the algorithm for star joins to evaluate a more general case of multiway joins, which are star connections of star joins and show that this can be done in polynomial time. In the general case, we show that testing emptiness of a multiway direction join is NPcomplete. This lower bound holds even when in the join predicate (1) only one attribute for each relation is involved, and (2) each spatial attribute occurs a bounded number of times. It implies that join evaluation in these cases is NPhard.
 Title
 On MultiWay Spatial Joins with Direction Predicates
 Book Title
 Advances in Spatial and Temporal Databases
 Book Subtitle
 7th International Symposium, SSTD 2001 Redondo Beach, CA, USA, July 12–15, 2001 Proceedings
 Pages
 pp 217235
 Copyright
 2001
 DOI
 10.1007/3540477241_12
 Print ISBN
 9783540423010
 Online ISBN
 9783540477242
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2121
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Christian S. Jensen ^{(1)}
 Markus Schneider ^{(2)}
 Bernhard Seeger ^{(3)}
 Vassilis J. Tsotras ^{(4)}
 Editor Affiliations

 1. Department of Computer Science, Aalborg University
 2. Praktische Informatik IV, FernUniversität Hagen
 3. Fachbereich Mathematik und Informatik, PhilippsUniversität Marburg
 4. Department of Computer Science and Engineering, University of California
 Authors

 Hongjun Zhu ^{(5)}
 Jianwen Su ^{(5)}
 Oscar H. Ibarra ^{(5)}
 Author Affiliations

 5. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA
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