Approximate Aggregate Queries Under Additive Inequalities
This addresses a computational bottleneck in learning applications where such queries are common, offering practical solutions for single-inequality cases but highlighting fundamental limits for more complex scenarios.
The paper tackles the problem of evaluating functional aggregation queries on relational data under additive inequalities, showing it is NP-hard even with one inequality and providing an efficient approximation algorithm with arbitrarily small relative error for many natural queries with one inequality, while proving that with two inequalities, approximation with bounded relative error is NP-hard.
We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly in many applications, particularly in learning applications. We give a relatively complete categorization of the computational complexity of such problems. We first show that the problem is NP-hard, even in the case of one additive inequality. Thus we turn to approximating the query. Our main result is an efficient algorithm for approximating, with arbitrarily small relative error, many natural aggregation queries with one additive inequality. We give examples of natural queries that can be efficiently solved using this algorithm. In contrast, we show that the situation with two additive inequalities is quite different, by showing that it is NP-hard to evaluate simple aggregation queries, with two additive inequalities, with any bounded relative error.