A Cube Algebra with Comparative Operations: Containment, Overlap, Distance and Usability

03/17/2022
by   Panos Vassiliadis, et al.
0

In this paper, we provide a comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces. We model cube queries and their semantics and define typical OLAP operators like Selections, Roll-Up, Drill-Down, etc. The model serves as the basis to offer the main contribution of this paper which includes theorems and algorithms for being able to associate data cube queries via comparative operations that are evaluated only on the syntax of the queries involved. Specifically, these operations include: (a) foundational containment, referring to the coverage of common parts of the most detailed level of aggregation of the multidimensional space, (b/c) same-level containment and intersection, referring to the inclusion/existence of common parts of the multidimensional space in two query results of the same aggregation levels, (d) query distance, referring to being able to assess the similarity of two queries in the same multidimensional space, and, (e) cube usability, i.e., the possibility of computing a new cube from a previous one, defined at a different level of abstraction.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/07/2018

Compact Representations of Event Sequences

We introduce a new technique for the efficient management of large seque...
research
10/18/2017

Typesafe Abstractions for Tensor Operations

We propose a typesafe abstraction to tensors (i.e. multidimensional arra...
research
09/03/2019

Online Analytical Processsing on Graph Data

Online Analytical Processing (OLAP) comprises tools and algorithms that ...
research
12/06/2022

Cube Interestingness: Novelty, Relevance, Peculiarity and Surprise

In this paper, we discuss methods to assess the interestingness of a que...
research
08/01/2020

GraphQL Live Querying with DynamoDB

We present a method of implementing GraphQL live queries at the database...
research
08/27/2018

NNCubes: Learned Structures for Visual Data Exploration

Visual exploration of large multidimensional datasets has seen tremendou...
research
12/19/2018

Beyond Roll-Up's and Drill-Down's: An Intentional Analytics Model to Reinvent OLAP (long-version)

This paper structures a novel vision for OLAP by fundamentally redefinin...

Please sign up or login with your details

Forgot password? Click here to reset