Banzhaf Values for Facts in Query Answering

by   Omer Abramovich, et al.

Quantifying the contribution of database facts to query answers has been studied as means of explanation. The Banzhaf value, originally developed in Game Theory, is a natural measure of fact contribution, yet its efficient computation for select-project-join-union queries is challenging. In this paper, we introduce three algorithms to compute the Banzhaf value of database facts: an exact algorithm, an anytime deterministic approximation algorithm with relative error guarantees, and an algorithm for ranking and top-k. They have three key building blocks: compilation of query lineage into an equivalent function that allows efficient Banzhaf value computation; dynamic programming computation of the Banzhaf values of variables in a Boolean function using the Banzhaf values for constituent functions; and a mechanism to compute efficiently lower and upper bounds on Banzhaf values for any positive DNF function. We complement the algorithms with a dichotomy for the Banzhaf-based ranking problem: given two facts, deciding whether the Banzhaf value of one is greater than of the other is tractable for hierarchical queries and intractable for non-hierarchical queries. We show experimentally that our algorithms significantly outperform exact and approximate algorithms from prior work, most times up to two orders of magnitude. Our algorithms can also cover challenging problem instances that are beyond reach for prior work.


The Impact of Negation on the Complexity of the Shapley Value in Conjunctive Queries

The Shapley value is a conventional and well-studied function for determ...

Computing the Shapley Value of Facts in Query Answering

The Shapley value is a game-theoretic notion for wealth distribution tha...

From Shapley Value to Model Counting and Back

In this paper we investigate the problem of quantifying the contribution...

A Simple Algorithm for Consistent Query Answering under Primary Keys

We consider the dichotomy conjecture for consistent query answering unde...

The Shapley Value of Tuples in Query Answering

We investigate the application of the Shapley value to quantifying the c...

Optimally Summarizing Data by Small Fact Sets for Concise Answers to Voice Queries

Our goal is to find combinations of facts that optimally summarize data ...

Neural Databases

In recent years, neural networks have shown impressive performance gains...

Please sign up or login with your details

Forgot password? Click here to reset