Uniform Range Partitioning

The main difference between the lifespan and the range is that the range does not contain those parts of the lifespan that are not covered by any interval in R or Q. In terms of the examples of chapter 7, where we analysed login-information to computers, this means that there might be times during which nobody was logged in to the computer(s), e.g. because of a downtime or a holiday. The idea behind partitioning the range rather than the lifespan is to omit such `gaps'  during which no temporal data is valid. Soo et al., for example, use this approach.

The complete IP-table provides sufficient information to identify the gaps, i.e. those parts of that do not belong to : the gaps are those areas between a t_j-1 and a t_j that are not overlapped by any intervals, i.e. . Thus all entries in with a 0 entry in the third column identify a gap.

In order to determine the breakpoint of a uniform range partition one has to calculate the length of the range, compute the target length of each segment by

Uniform range partitioning, as outlined in figure 9.4, works well with complete IP-tables. However, we might not be able to identify the gaps when using an incomplete IP-table because the condensation  process might have collapsed a gap into a condensed timepoint (see sections 7.3.3 and 7.3.4). Therefore the result will be close to the one achieved by uniform lifespan partitioning.

In practice, one has to doubt whether uniform range partitioning achieves much better results than uniform lifespan partitioning as one can expect the range to be close to the lifespan in many applications. Also, algorithms for uniform range partitioning, such as the one in figure 9.4 or ChooseIntervals in [Soo et al., 1994], are very inefficient in comparison to the one in figure 9.2. This fact presumably outweighs the small benefit that can be drawn from partitioning the range rather than the lifespan.