Sensitivity Analysis for Declarative Relational Query Languages with Ordinal Ranks

TL;DR

This paper introduces sensitivity analysis for relational query results with ordinal ranks, demonstrating that small data changes do not significantly alter query outcomes in this extended model.

Contribution

It extends Codd's relational model by incorporating ordinal ranks and analyzes the stability of query results under data perturbations.

Findings

Ranks are insensitive to small data changes

Small input variations do not cause large output changes

Sensitivity analysis applies to ordinal ranked data

Abstract

We present sensitivity analysis for results of query executions in a relational model of data extended by ordinal ranks. The underlying model of data results from the ordinary Codd's model of data in which we consider ordinal ranks of tuples in data tables expressing degrees to which tuples match queries. In this setting, we show that ranks assigned to tuples are insensitive to small changes, i.e., small changes in the input data do not yield large changes in the results of queries.