Linear Programs with Conjunctive Database Queries

TL;DR

This paper introduces LP(CQ), a framework for optimizing linear programs based on conjunctive query answers, with an efficient algorithm that reduces variable count by exploiting query structure, applicable to resource delivery, privacy, and data mining.

Contribution

The paper proposes LP(CQ), a novel language for linear programs dependent on conjunctive query answers, and provides an efficient algorithm leveraging hypertree decompositions to reduce problem size.

Findings

The algorithm constructs smaller linear programs with the same optimal value.

LP(CQ) effectively models resource allocation, privacy, and data mining problems.

Applications demonstrate practical utility of the proposed approach.

Abstract

In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions depend on the answer sets of conjunctive queries. We contribute an efficient algorithm for solving programs in a fragment of LP(CQ). The natural approach constructs a linear program having as many variables as there are elements in the answer set of the queries. Our approach constructs a linear program having the same optimal value but fewer variables. This is done by exploiting the structure of the conjunctive queries using generalized hypertree decompositions of small width to factorize elements of the answer set together. We illustrate the various applications of LP(CQ) programs on three examples: optimizing deliveries of resources, minimizing noise for differential privacy, and computing the s-measure of patterns in graphs as needed for data mining.