7±2 criteria for assessing and comparing spatial data structures

Abstract

Spatial data structures have evolved under the influence of several forces: 1) Database technology, with its emphasis on modeling and logical organization; 2) the long history of data structures developed in response to requirements from other applications; and 3) the recent rapid progress in computational geometry, which has identified typical queries and access patterns to spatial data. Rather than attempting a comprehensive survey of many spatial data structures recently developed, we aim to identify the key issues that have created them, their common characteristics, the requirements they have to meet, and the criteria for assessing how well these requirements are met. As a guideline for tackling these general goals, we begin with a brief history and recall how past requirements from other applications have shaped the development of data structures. Starting from the very early days, five major types of applications generated most of the known data structures. But the requirements of these applications do not include one that is basic to spatial data: That objects are embedded in Euclidian space, and access is mostly determined by location in space.

We present six specifically geometric requirements spatial data structures must address. Sections 3, 4, 5 discuss the mostly static aspects of how space is organized, and how objects are represented and embedded in space. Sections 6, 7, 8 consider the dynamic aspects of how objects are processed. We differentiate three types of processing, of increasing complexity, that call for different solutions: common geometric transformations such as translation and rotation; proximity search, and traversal of the object by different types of algorithms. Together with the general requirement of effective implementability, we propose these seven criteria as a profile for assessing spatial data structures. This survey leads us to two main conclusions: 1) That the current emphasis on comparative search trees is perhaps unduly influenced by the great success balanced trees enjoyed as a solution to the requirements of older applications that rely on single-key access, and 2) that spatial data structures are increasingly of the ‘metric’ type based on radix partitions of space.