The general idea of tilted time frames is to store snapshots at different levels
of granularity depending on how old these snapshots are. The more time has
passed, the larger the gap between two consecutive snapshots will be. Tilted
time frames were introduced in [5], where the pattern of storing snapshots is
aligned with the natural time, that means in the most recent quarter we take
one snapshot per minute, in the most recent hour one snapshot per quarter
and so on.
Older snapshots have to be maintained regularly in this model. There
are several ways of dealing with a transition from one level of granularity
to another depending on how the snapshots are structured. One way is
by looking independently at each granularity level and dropping the oldest
snapshot whenever a new snapshot for that particular level arrives. This
concept is used in CluStream which we will discuss in section 4.2.
Another way is by merging snapshots. Snapshots of a finer granularity are
accumulated until they contain enough data to form a snapshot for the next
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12 Chapter 4. Time Frames
smaller level of detail. Using a logarithmic time window where the time gap
between snapshots increases by a factor of 2 between each level, we can show
that the amortized number of maintenance operations is limited to O(1)