Indexing Interpolated Time Sequences

A time sequence is a discrete sequence of values, e.g. temperature measurements, varying over time. By applying an interpolation function a discrete time sequence can be coerced into a continues function over time, F(t), which we call an interpolated time sequence. Many applications need to deal with querying interpolated time sequences. Simple queries involve finding F(t’) for a given time point t’, which are easy to support using regular ordered indexes. The main contribution of this paper is a new index structure, the interpolation index (IP-index) which supports efficient retrievals of those time points t where F(t) = v’ for a given v’, i.e. efficient computation of interpolated inverse queries, F-1(v’). Performance measures show that the IPindex radically improves the search time for interpolated inverse queries. It is also shown that the insertion time of the IPindex for most periodic time sequences has an upper limit, and for largely monotonic sequences it is logarithmic.