On the complexity of BV-tree updates

Abstract

We have shown in this paper how logarithmic exact-match access and update complexity can be maintained in a BV-tree representation. The price paid for guaranteed dynamic performance (i.e. performance which does not degrade over time for a given data set) is that the demotion of entries which no longer represent guards may be postponed. In the worst case this could require a substantial increase in the size of higher level index nodes in order to maintain a constant level of performance for a given data set.

However, although we have as yet no clear idea how the probability of occurrence of the worst case might be theoretically assessed, it intuitively seems to be an inconceivably improbable event. It is also difficult to see how particular data distributions, or the order of insertion or deletion could significantly affect this probability. Experimental performance studies are needed to establish this intuition more solidly. Most importantly, however, the index implementor can choose to guarantee a constant performance level by accommodating increased page sizes when necessary, or accept the remote but unpredictable risk of lower performance within a simpler implementation of fixed page size.