Efficient Management of 2-d Interval Relations

The term interval is quite generic. Time intervals mark the duration of events (the lifespan of a person). Alphabetic intervals have many applications (family names in the range A-C). Given the wide use of intervals, their handling is of major importance. However, there is a number of problems which relate to their management. Such of them were initially identified in research in temporal databases. In particular, the necessity to support temporal data led to the formalisation of many distinct temporal extensions to the relational model [1]. In spite however of the major differences between the various modelling approaches, one characteristic, common to almost all of them, is that the ordinary projection, set-union and set-difference operations are adapted appropriately, in all of them, so as to apply appropriately to data incorporating time intervals. Next, it was identified that the same problems arise in the management of certain types of spatial data [2, 3], and this gave recently rise in research in spatiolemporal databases [4]. The Interval-Extended Relational Model (IXRM) was defined to handle them in a uniform way. In this paper we investigate the properties of the IXRM operations and propose efficient algorithms for the above operations. Our work restricts to relations with two pure interval attributes. The algorithms have been based on the geometric interpretation of the contents of pure interval attributes and improve substantially the time and space requirements. The remainder of this work is as follows: In section 2 we identify certain problems concerning the management of interval data. In section 3 we present briefly the IXRM and investigate the properties of its operations. In section 4 we make use of these properties and provide efficient algorithms. Conclusions are drawn in the last section.