Exploring spatial datasets with histograms

Abstract

As online spatial datasets grow both in number and sophistication, it becomes increasingly difficult for users to decide whether a dataset is suitable for their tasks, especially when they do not have prior knowledge of the dataset. In this paper, we propose browsing as an effective and efficient way to explore the content of a spatial dataset. Browsing allows users to view the size of a result set before evaluating the query at the database, thereby avoiding zero-hit/mega-hit queries and saving time and resources. Although the underlying technique supporting browsing is similar to range query aggregation and selectivity estimation, spatial dataset browsing poses some unique challenges. In this paper, we identify a set of spatial relations that need to be supported in browsing applications, namely, the contains, contained and the overlap relations. We prove a lower bound on the storage required to answer queries about the contains relation accurately at a given resolution. We then present three storage-efficient approximation algorithms which we believe to be the first to estimate query results about these spatial relations. We evaluate these algorithms with both synthetic and real world datasets and show that they provide highly accurate estimates for datasets with various characteristics.

A Mobile Data Management Architecture for Interoperability of Resource and Context Data

“…Most notably it is not required to examine all cells that overlap with the query region. Beigel and Tanin [1998], Sun et al [2006] and Lin et al [2003] proposed cell density approaches based on the Euler Formula [Harary, 1969], allowing the topological relations contains, contained, overlap, and disjoint. PostGIS 7 uses a comparatively simple approach based on cell density.…”

Summarizing Spatial Relations – A Hybrid Histogram

“…In many applications, however, users are more interested in summarized information instead of objects' individual properties . Especially with the availability of a huge collection of on-line spatial data [1,2,3] (e.g. large digital libraries/archives), it becomes extremely important to support interactive queries by query preview [4,1].…”

“…They group "similar" objects together into one bucket for estimating the number of disjoint and non-disjoint objects with respect to window query. Techniques based on cell density [4,11,3,8] propose to divide the object space evenly into a number of disjoint cells, and record object density information in each cell. Cumulative density based approach [11] and Euler histogram [4] can provide the exact solutions against the aligned window query (to be defined in Section 2) for non-disjoint and disjoint topological relations only.…”

“…Cumulative density based approach [11] and Euler histogram [4] can provide the exact solutions against the aligned window query (to be defined in Section 2) for non-disjoint and disjoint topological relations only. Euler-Approx [3] and Multiscale Histogram [8] substantially extended the Euler histogram techniques for summarizing the 4 important binary topological relations: "contains", "contained ", "overlap", and "disjoint" ( to be defined in Section 2) against the aligned window query.…”

Analysis of predictive spatio-temporal queries

“…An et al [2001] maintains statistics about objects' edges and corners, while Belussi and Faloutsos [1998] and Faloutsos et al [2000] apply power laws. Sun et al [2002a] studies join selectivity restricted in a part of the data-space, and Mamoulis and Papadias [2001] addresses multi-way spatial join selectivity.…”