Linear Programs with Conjunctive Queries
Abstract
In this paper, we study the problem of optimizing a linear program
whose variables are 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 naive approach constructs a
linear program having as many variables as 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 hypertree decompositions of
small width to group 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.
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