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Beyond Uniformity and Independence : Analysis of R-trees Using the Concept of Fractal Dimension

Summary: Introduce fractal dimension to quantify deviation from uniformity; show many real spatial point sets behave as fractals with non-integer dimensions. Use fractal dimension + cardinality to derive a formula predicting R-tree range-query I/Os for skewed data (error usually <5–10%), enabling analysis and optimizer estimates without uniformity/independence assumptions. (summarized by gpt-5-mini on Feb 09 2026)

Paper ID
1011
Venue
PODS
Year
1994
Pagerank
0.00013901031
Overall Rank
1,114 | 92.26%
DOI
-

Incoming Non-self Citations Over Time

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Incoming Citations (Sorted by Pagerank)

Showing 20 of 20 citing papers.

Rank Citing Paper Year Venue Pagerank
79 A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces 1998 VLDB 0.00056242144
195 Optimizing Queries over Multimedia Repositories 1996 SIGMOD 0.00035406558
242 Generalized Search Trees for Database Systems (Extended Abstract) 1995 VLDB 0.00031110894
1,488 On the Analysis of Indexing Schemes 1997 PODS 0.00011699446
1,528 A Model for the Prediction of R-tree Performance 1996 PODS 0.00011497734
1,608 MindReader: Querying databases through multiple examples 1998 VLDB 0.00011151257
1,811 A Cost Model for Similarity Queries in Metric Spaces 1998 PODS 0.00010467197
1,983 Optimizing Multidimensional Index Trees for Main Memory Access 2001 SIGMOD 9.8638201e-05
2,974 Estimating the Selectivity of Spatial Queries Using the 'Correlation' Fractal Dimension 1995 VLDB 7.789769e-05
3,255 A Revised R*-tree in Comparison with Related Index Structures 2009 SIGMOD 7.3160522e-05
3,417 General Match: A Subsequence Matching Method in Time-Series Databases Based on Generalized Windows 2002 SIGMOD 7.1195863e-05
3,527 Analysis of n-dimensional Quadtrees Using the Hausdorff Fractal Dimension 1996 VLDB 7.0073154e-05
3,900 Tight bounds for 2-dimensional indexing schemes 1998 PODS 6.6518011e-05
5,013 A Lower Bound Theorem for Indexing Schemes and its Application to Multidimensional Range Queries 1998 PODS 5.7598528e-05
6,161 Spatial Join Selectivity Using Power Laws 2000 SIGMOD 5.1753664e-05
8,323 Towards Practical Constraint Databases (Extended Abstract) 1996 PODS 4.5435639e-05
8,819 Modeling Skew in Data Streams 2006 SIGMOD 4.4421123e-05
9,143 Similarity Query Processing Using Disk Arrays 1998 SIGMOD 4.3850454e-05
9,207 Rethinking Choices for Multi-dimensional Point Indexing: Making the Case for the Often Ignored Quadtree 2007 CIDR 4.3733038e-05
10,165 Fast-Convergent Proximity Graphs for Approximate Nearest Neighbor Search 2026 SIGMOD 4.1945683e-05
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Outgoing Citations (Sorted by Pagerank)

Showing 10 of 10 cited papers.

Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.

Rank Cited Paper Year Venue Pagerank
2 R-Trees: A Dynamic Index Structure For Spatial Searching 1984 SIGMOD 0.0032169493
6 The R*-tree: An Efficient and Robust Access Method for Points and Rectangles 1990 SIGMOD 0.0016162015
24 The R+-Tree: A Dynamic Index For Multi-Dimensional Objects 1987 VLDB 0.00083378538
56 Direct Spatial Search on Pictorial Databases Using Packed R-trees 1985 SIGMOD 0.00065631356
76 Spatial Query Processing in an Object-Oriented Database System 1986 SIGMOD 0.00057303551
99 On the Propagation of Errors in the Size of Join Results 1991 SIGMOD 0.00050022914
116 Equi-Depth Histograms For Estimating Selectivity Factors For Multi-Dimensional Queries 1988 SIGMOD 0.00046148737
638 On B-tree Indices for Skewed Distributions 1992 VLDB 0.00018798677
725 Optimization Strategies for Spatial Query Processing 1991 VLDB 0.00017529198
2,030 Analysis Of Object Oriented Spatial Access Methods 1987 SIGMOD 9.7378136e-05
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7,054 Theoretically Optimal and Empirically Efficient R-trees with Strong Parallelizability 2018 VLDB 4.8496866e-05
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6 The R*-tree: An Efficient and Robust Access Method for Points and Rectangles 1990 SIGMOD 0.0016162015
9,767 Adaptive Indexing of Objects with Spatial Extent 2023 VLDB 4.2856106e-05
2,586 Segment Indexes: Dynamic Indexing Techniques for Multi-Dimensional Interval Data 1991 SIGMOD 8.4928908e-05
5,982 Modeling skewed distributions using multifractals and the '80-20 law' 1996 VLDB 5.2446136e-05
2,030 Analysis Of Object Oriented Spatial Access Methods 1987 SIGMOD 9.7378136e-05
1,528 A Model for the Prediction of R-tree Performance 1996 PODS 0.00011497734
3,527 Analysis of n-dimensional Quadtrees Using the Hausdorff Fractal Dimension 1996 VLDB 7.0073154e-05
2,974 Estimating the Selectivity of Spatial Queries Using the 'Correlation' Fractal Dimension 1995 VLDB 7.789769e-05