# Solving linear programs on factorized databases

## TL;DR

This paper introduces a method to solve linear programming problems over database query answers by exploiting query structure, significantly reducing the problem size when the answer set is large, especially for queries with bounded fractional hypertree width.

## Contribution

It presents a generic approach to rewrite linear programs based on factorized database representations, leveraging query structure to improve efficiency.

## Key findings

- Rewrites linear programs to depend on factorized database size
- Reduces linear program size for queries with bounded fractional hypertree width
- Enables solving large LPs efficiently using query structure

## Abstract

A typical workflow for solving a linear programming problem is to first write a linear program parametrized by the data in a language such as Math GNU Prog or AMPL then call the solver on this program while providing the data. When the data is extracted using a query on a database, this approach ignores the underlying structure of the answer set which may result in a blow-up of the size of the linear program if the answer set is big. In this paper, we study the problem of solving linear programming problems whose variables are the answers to a conjunctive query. We show that one can exploit the structure of the query to rewrite the linear program so that its size depends only on the size of the database and not on the size of the answer set. More precisely, we give a generic way of rewriting a linear program whose variables are the tuples in Q(D) for a conjunctive query Q and a database D into a linear program having a number of variables that only depends on the size of a factorized representation of Q(D), which can be much smaller when the fractional hypertree width of Q is bounded.