A multidimensional data model with subcategories for flexibly capturing summarizability

Abstract

In multidimensional (MD) databases and data warehouses we commonly prefer instances that have summarizable dimensions. This is because they have good properties for query answering. Most typically, with summarizable dimensions, precomputed and materialized aggregate query results at lower levels of the dimension hierarchy can be used to correctly compute results at higher levels of the same hierarchy, improving efficiency. Being summarizability such a desirable property, we argue that some established MD models cannot properly model the summarizability condition, and this is a consequence of the limited expressive power of the modeling languages. We propose an extension to the Hurtado-Meldelzon (HM) MD model with subcategories, the EHM model, and show that it allows to capture the summarizability. We propose an efficient algorithm that, for a given cube view (i.e. MD aggregate query) in an EHM database, determines from which minimal subset of precomputed cube views it can be correctly computed. Finally, we show how the EHM can be implemented with minor modifications to the familiar ROLAP schemas.

Detecting summarizability in OLAP

“…This will belong to our future research. Value-per-unit or 2) Stock Non-additive 1) item price, cost per unit manufactured; 2) temperature, pressure, speed A factor used to converted measure units Conversion Factor Value-per-unit Non-additive Exchange rate 5. Summarizability of measures created by combining existing measures using arithmetic operations is not included in existing research.…”

“…Ariyan and Bertossi [1] focus on the aspect of summarizability relevant to determining whether an aggregation computed at a low level in an aggregation hierarchy can be used to compute an aggregation at a higher level in that hierarchy, thereby avoiding accessing the raw data. Ariyan and Bertossi propose extending Hurtado et al's multidimensional model in a way which facilitates the adaptation of some problematic dimension schemata so that the properties of their aggregation hierarchies become compatible with summarizability.…”

Ontological Multidimensional Data Models and Contextual Data Quality

“…I . 7 A homomorphism is a structure-preserving mapping, h: C ∪ N → C ∪ N , between two instances I and I for schema R such that: (a) t ∈ C implies h(t) = t, and (b) for every ground atom P( t): if P( t) ∈ I , then P(h( t)) ∈ I .…”

“…A Datalog program Π for schema R is a nite set of non-existential rules, i.e. as in (7) but without ∃-variables. Some of the predicates in Π are extensional, i.e.…”

“…A Datalog + program may contain, in addition to (non-existential) Datalog rules, also existential rules rules of the form (7), and constraints of the forms ( 8) and (9). A Datalog + program has Ontological MD Data Models and Contextual Data ality 1:11 an extensional database D. In a Datalog + program Π, unlike plain Datalog, predicates are not necessarily partitioned into extensional and intentional ones: any predicate may appear in the head of a rule.…”