Beyond Uniformity and Independence: Analysis of R-Trees Using the Concept of Fractal Dimension",

dc.contributor.authorFaloutsos, Christosen_US
dc.contributor.authorKamel, Ibrahimen_US
dc.description.abstractWe propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, star coordinates from NASA's Infrared-Ultraviolet Explorer etc.) we provide evidence that real data indeed are skewed, and, moreover, we show that they behave as mathematical fractals, with a measurable, non-integer fractal dimension. Armed with this tool, we then show its practical use in predicting the performance of spatial access methods, and specifically of the R-trees. We provide the {\em first} analysis of R-trees for skewed distributions of points: We develop a formula that estimates the number of disk accesses for range queries, given only the fractal dimension of the point set, and its count. Experiments on real data sets show that the formula is very accurate: the relative error is usually below 5\%, and it rarely exceeds 10\%. We believe that the fractal dimension will help replace the uniformity and independence assumptions, allowing more accurate analysis for {\em any} spatial access method, as well as better estimates for query optimization on multi-attribute queries. NOTE - Appeared in PODS 1994. Christos Faloutsos and Ibrahim Kamel. "Beyond Uniformity and Independence: Analysis of R-Trees Using the Concept of Fractal Dimension", Proc. ACM SIGACT-SIGMOD-SIGART PODS. Minneapolis, MN (May 1994), pp. 4-13. (Also cross-referenced as UMIACS-TR-93-130)en_US
dc.format.extent999253 bytes
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3198en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-93-130en_US
dc.titleBeyond Uniformity and Independence: Analysis of R-Trees Using the Concept of Fractal Dimension",en_US
dc.typeTechnical Reporten_US


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