Relational Algebra for In-Database Process Mining

The execution logs that are used for process mining in practice are often obtained by querying an operational database and storing the result in a flat file. Consequently, the data processing power of the database system cannot be used anymore for this information, leading to constrained flexibility in the definition of mining patterns and limited execution performance in mining large logs. Enabling process mining directly on a database - instead of via intermediate storage in a flat file - therefore provides additional flexibility and efficiency. To help facilitate this ideal of in-database process mining, this paper formally defines a database operator that extracts the 'directly follows' relation from an operational database. This operator can both be used to do in-database process mining and to flexibly evaluate process mining related queries, such as: "which employee most frequently changes the 'amount' attribute of a case from one task to the next". We define the operator using the well-known relational algebra that forms the formal underpinning of relational databases. We formally prove equivalence properties of the operator that are useful for query optimization and present time-complexity properties of the operator. By doing so this paper formally defines the necessary relational algebraic elements of a 'directly follows' operator, which are required for implementation of such an operator in a DBMS

Nested Queries and Quantifiers in an Ordered Context

We present algebraic equivalences that allow to unnest nested algebraic expressions for order-preserving algebraic operators. We illustrate how these equivalences can be applied successfully to unnest nested queries given in the XQuery language. Measurements illustrate the performance gains possible by our approach

Towards an Efficient Evaluation of General Queries

Database applications often require to evaluate queries containing quantifiers or disjunctions, e.g., for handling general integrity constraints. Existing efficient methods for processing quantifiers depart from the relational model as they rely on non-algebraic procedures. Looking at quantified query evaluation from a new angle, we propose an approach to process quantifiers that makes use of relational algebra operators only. Our approach performs in two phases. The first phase normalizes the queries producing a canonical form. This form permits to improve the translation into relational algebra performed during the second phase. The improved translation relies on a new operator - the complement-join - that generalizes the set difference, on algebraic expressions of universal quantifiers that avoid the expensive division operator in many cases, and on a special processing of disjunctions by means of constrained outer-joins. Our method achieves an efficiency at least comparable with that of previous proposals, better in most cases. Furthermore, it is considerably simpler to implement as it completely relies on relational data structures and operators

SEMISTRUCTURED PROBABILISTIC OBJECT QUERY LANGUAGE (A Query Language for Semistructured Probabilistic Data)

This work presents SPOQL, a structured query language for Semistructured Probabilistic Object (SPO) model [4]. The original query language for semistructured probabilistic database management system [20], SP-Algebra [4], has limitations such as complex functional notation and unfamiliarity to application programmers. SPOQL alleviates these problems by providing a user friendly and familiar SQL-like declarative syntax for writing queries against SPDBMS. We show that parsing SPOQL queries is a more involving task than parsing SQL queries. We describe the evaluation algorithm for SPOQL queries that we have implemented

Relational Approach to Logical Query Optimization of XPath

To be able to handle the ever growing volumes of XML documents, effective and efficient data management solutions are needed. Managing XML data in a relational DBMS has great potential. Recently, effective relational storage schemes and index structures have been proposed as well as special-purpose join operators to speed up querying of XML data using XPath/XQuery. In this paper, we address the topic of query plan construction and logical query optimization. The claim of this paper is that standard relational algebra extended with special-purpose join operators suffices for logical query optimization. We focus on the XPath accelerator storage scheme and associated staircase join operators, but the approach can be generalized easily

Relation partition algebra — mathematical aspects of uses and part-of relations

AbstractManaging complexity in software engineering involves modularisation, grouping design objects into modules, subsystems, etc. This gives rise to new design objects with new ‘use relations’. The lower-level design objects relate to these in a ‘part-of’ relation. But how do ‘use relations’ at different levels of the ‘part-of hierarchy’ relate? We formalise our knowledge on uses and part-of relations, looking for mathematical laws about relations and partitions. A central role is played by an operator /. For a “uses” relation r on a set of objects X and a partitioning into modules viewed as an equivalence θ, we form a relation rθ on the set Xθ. We adopt an axiomatic point of view and investigate a variety of models, corresponding to different abstraction mechanisms and different ways of relating high- and low-level uses relations