Multi-dimensional Aggregation for Temporal Data

Abstract

Abstract. Business Intelligence solutions, encompassing technologies such as multi-dimensional data modeling and aggregate query processing, are being applied increasingly to non-traditional data. This paper extends multi-dimensional aggregation to apply to data with associated interval values that capture when the data hold. In temporal databases, intervals typically capture the states of reality that the data apply to, or capture when the data are, or were, part of the current database state. This paper proposes a new aggregation operator that addresses several challenges posed by interval data. First, the intervals to be associated with the result tuples may not be known in advance, but depend on the actual data. Such unknown intervals are accommodated by allowing result groups that are specified only partially. Second, the operator contends with the case where an interval associated with data expresses that the data holds for each point in the interval, as well as the case where the data holds only for the entire interval, but must be adjusted to apply to sub-intervals. The paper reports on an implementation of the new operator and on an empirical study that indicates that the operator scales to large data sets and is competitive with respect to other temporal aggregation algorithms.

Parsimonious temporal aggregation

“…In a similar vein, the multi-dimensional temporal aggregation operator [2] generalizes previous temporal aggregation operators. Two different semantics are distinguished.…”

“…Various forms of temporal aggregation have been studied in the past, including instant temporal aggregation (ITA), moving-window temporal aggregation (MWTA), and span temporal aggregation (STA) [2,7,8,12,13,16]. They differ mainly in how the time line is partitioned.…”

“…Figure 7 shows the integrated gPTA algorithm. We adapted the ITA algorithm in [2] to produce the ITA result tuples one by one, which does not change its performance and space requirements. Figure 8 depicts the contents of the heap each time a new ITA result tuple is processed.…”

“…Span temporal aggregation (STA) [2,7] allows to control the result size by permitting an application to specify the time intervals for which to report a result tuple, e.g., for each year from 2000 to 2005. For each of these intervals a result tuple is produced by aggregating over all argument tuples that overlap that interval.…”

Storing and processing temporal data in a main memory column store

“…Since Snodgrass' definition of the temporal data model [14], there has been a large body of work in this area, summarized in [12,4]. This related work covers proposals for index structures (e.g., multi-version Btrees [1]) and algorithms for certain kinds of queries (e.g., temporal aggregation [10,2] and temporal joins [4,15]). In most related work the focus was on disk based structures, optimizing for I/O behavior.…”