Efficient Computation of Parsimonious Temporal Aggregation

Abstract

Parsimonious temporal aggregation (PTA) has been introduced to overcome limitations of previous temporal aggregation operators, namely to provide a concise yet data sensitive summary of temporal data. The basic idea of PTA is to first compute instant temporal aggregation (ITA) as an intermediate result and then to merge similar adjacent tuples in order to reduce the final result size. The best known algorithm to compute a correct PTA result is based on dynamic programming (DP) and requires $\mathcal {O}(n^2)$ space to store a so-called split point matrix, where n is the size of the intermediate data. The matrix stores the split points between which the intermediate tuples are merged.

In this paper, we propose two optimizations of the DP algorithm for PTA queries. The first optimization is termed diagonal pruning and identifies regions of the matrix that need not to be computed. This reduces the runtime complexity. The second optimization addresses the space complexity. We observed that only a subset of the elements in the split point matrix are actually needed. Therefore, we propose to replace the split point matrix by a so-called split point graph, which stores only those split points that are needed to restore the optimal PTA solution. This step reduces the memory consumption. An empirical evaluation shows the effectiveness of the two optimizations both in terms of runtime and memory consumption.