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Banzhaf Values for Facts in Query Answering

Authors:

Omer Abramovich,

Dan OlteanuAuthors Info & Claims

Proceedings of the ACM on Management of Data, Volume 2, Issue 3

Article No.: 123, Pages 1 - 26

https://doi.org/10.1145/3654926

Published: 30 May 2024 Publication History

Abstract

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.

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Cited By

Bertossi LAzua F(2024)The Generalized Causal-Effect Score in Data Management (short paper)Proceedings of the Conference on Governance, Understanding and Integration of Data for Effective and Responsible AI10.1145/3665601.3669843(32-35)Online publication date: 9-Jun-2024
https://dl.acm.org/doi/10.1145/3665601.3669843
Karmakar PMonet MSenellart PBressan S(2024)Expected Shapley-Like Scores of Boolean functions: Complexity and Applications to Probabilistic DatabasesProceedings of the ACM on Management of Data10.1145/36515932:2(1-26)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651593

Index Terms

Banzhaf Values for Facts in Query Answering
1. Information systems
  1. Data management systems
    1. Database design and models
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Database theory
      1. Data provenance

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Published In

cover image Proceedings of the ACM on Management of Data

Proceedings of the ACM on Management of Data Volume 2, Issue 3

SIGMOD

June 2024

1953 pages

EISSN:2836-6573

DOI:10.1145/3670010

Editor:
Divyakant Agrawal
UC Santa Barbara, United States

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Copyright © 2024 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 May 2024

Published in PACMMOD Volume 2, Issue 3

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Cited By

Bertossi LAzua F(2024)The Generalized Causal-Effect Score in Data Management (short paper)Proceedings of the Conference on Governance, Understanding and Integration of Data for Effective and Responsible AI10.1145/3665601.3669843(32-35)Online publication date: 9-Jun-2024
https://dl.acm.org/doi/10.1145/3665601.3669843
Karmakar PMonet MSenellart PBressan S(2024)Expected Shapley-Like Scores of Boolean functions: Complexity and Applications to Probabilistic DatabasesProceedings of the ACM on Management of Data10.1145/36515932:2(1-26)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651593

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