Dynamic and Hierarchical Spatial Access Method using Integer Searching

Kyoosang Cho, Yijie Han, Yugyung Lee, E. K. Park

Abstract: Dynamic and complex computation in the area of Geographic Information System (GIS) or Mobile Computing System involves huge amount of spatial objects such as points, boxes, polygons, etc and requires a scalable data structure and an efficient management tool for this information. In this paper, for a dynamic management of spatial objects, we construct a hierarchical dynamic data structure, called an IST/OPG hierarchy, which may overcome some limitations of existing Spatial Access Methods (SAMs). The hierarchy is constructed by combining three primary components: (1) Minimum Boundary Rectangle (MBR), which is the most widely used method among SAMs; (2) the population-based domain slicing, which is modified from the Grid File [14]; (3) extended optimal Integer Searching algorithm [4]. For dynamic management of spatial objects in the IST/OPG hierarchy, a number of primary and supplementary operations are introduced. This paper includes a comparative analysis of our approach with previous SAMs, such as R-Tree, R+-Tree and R*-Tree and QSF-Tree. The results of analysis show that our approach is better than other SAMs in construction and query time and space requirements. Specifically, for a given search domain with n objects, our query operations yield $O($ \scriptsize $\sqrt {\frac {\log n} {\log\log n}}$\normalsize $)$ compared to $O(\log n)$ of the fast SAM and an IST/OPG hierarchy containing $n$ objects can be constructed in $O(n$ \scriptsize $\sqrt {\frac {\log n}{\log\log n}}$\normalsize $)$ time and O(n) space.