Indexing Valid Time Intervals

To support temporal operators and to increase the efficiency of temporal queries, indexing based on temporal attributes is required. We consider the problem of indexing the temporal dimension in valid time databases. We assume that the temporal information of data objects are represented as valid time intervals that have to be managed dynamically by an efficient index structure. Unlike the time intervals in transaction time databases, valid time intervals can be inserted, deleted, and modified at any point in time. Furthermore, their lifespans can go beyond the current time point and extend into the future. We propose an indexing scheme that uses augmented B+trees called Interval B+trees for indexing a dynamic set of valid time intervals. Interval B+trees (IB+trees) use beginning points of the intervals as key points and keep maximum end point information of its subtrees for each internal node. We introduce an algorithm to apply time-splits at the leaf level of the IB+tree that would partition long valid time intervals into disjoint subintervals and distribute them among several leaf nodes to increase efficiency of search operation, especially for timeslice queries. We compared IB+trees with time-splits to one dimensional R-trees and observed that while their performances for timeslice queries are comparable, IB+trees are far more superior for many temporal queries that are based on beginning points of time intervals. This is expected as the IB+trees use the beginning points of intervals as keys and therefore support such queries naturally. We also show the extensions to our indexing scheme for handling open ended valid time intervals (valid time intervals whose lifespans extend into future indefinitely), and valid time intervals whose end points move along the current timeline.