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arXiv 1901.03633cs.DB
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在分解数据库上求解线性规划

Solving linear programs on factorized databases

Florent Capelli, Nicolas Crosetti, Joachim Niehren, Jan Ramon

摘要:

解决线性规划问题的典型工作流程是首先用Math GNU Prog或AMPL等语言编写一个由数据参数化的线性程序,然后在提供数据的同时调用该程序的求解器。当使用数据库上的查询提取数据时,这种方法忽略了答案集的底层结构,如果答案集很大,则可能导致线性规划的大小爆炸。本文研究了变量为合取查询答案的线性规划问题的求解问题。我们表明,可以利用结构的查询重写线性规划,使其大小仅取决于数据库的大小,而不是答案集的大小。更确切地说,我们给出了一种通用的方法,将其变量为Q(D)中的元组的线性规划重写为具有仅取决于Q(D)的因子分解表示的大小的变量的线性规划,当Q的分数超树宽度有界时,Q(D)的因子分解表示可以小得多。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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