On the consistency of cardinal direction constraints

A survey of qualitative spatial representations

“…It has been proved that composition in CDC is weak composition (Skiadopoulos and Koubarakis, 2004) and consistency checking a set of unrestricted CDC constraints is NP-complete (Skiadopoulos and Koubarakis, 2005;. However by introducing the rectangle algebra into CDC, a tractable subset including 36 base rectangular relations has been identified (Navarrete and Sciavicco, 2006); the rectangle-based inverting rules (Chen et al, 2010a) and composition(Chen et al, 2010b) are given, and these can be easily extended to cubic space.…”

“…An O(n 5 ) and an improved cubic consistency checking algorithm for the basic CDC constraints are given in (Skiadopoulos and Koubarakis, 2005) and respectively. It has been proved that composition in CDC is weak composition (Skiadopoulos and Koubarakis, 2004) and consistency checking a set of unrestricted CDC constraints is NP-complete (Skiadopoulos and Koubarakis, 2005;.…”

Computing and managing cardinal direction relations

“…This offers a more precise and expressive model than previous approaches that approximate both extended regions using points or MBBs [5], [9], [12], [14]. In this paper, we employ the cardinal direction model presented in [23], [25] because it is formally defined and can be applied to a wide set of regions (e.g., disconnected regions and regions with holes). Additionally, we also study cardinal direction relations with percentages [6].…”

“…Cardinal direction relations are qualitative spatial relations characterizing the relative position of a region with respect to another (e.g., region a is north of region b). Our starting point is the cardinal direction framework presented in [6], [24], [25]. The underlining idea of this framework is quite simple.…”

“…Among these research topics, qualitative spatial reasoning has received a lot of attention in the areas of Geographic Information Systems [3], [5], Artificial Intelligence [2], [17], Databases [14], and Multimedia [19]. Several kinds of useful spatial relations have been studied so far, e.g., topological relations [2], [3], [17], directional relations [6], [9], [12], [24], [25], and qualitative distance relations [4], [30]. The uttermost aim in these lines of research is to define new categories of spatial operators as well as to build efficient algorithms for the automatic processing of queries using such operators.…”