Aggregated Deletion Propagation for Counting Conjunctive Query Answers

TL;DR

This paper studies the problem of efficiently removing a specified number of output tuples from conjunctive query results by minimally deleting input tuples, providing complexity characterizations and practical algorithms.

Contribution

It introduces the Aggregated Deletion Propagation problem, characterizes its polynomial-time solvability, and offers practical heuristics with experimental evaluation.

Findings

Polynomial-time algorithm for certain query classes

Structural characterization of NP-hard instances

Practical heuristic algorithms with experimental results

Abstract

We investigate the computational complexity of minimizing the source side-effect in order to remove a given number of tuples from the output of a conjunctive query. This is a variant of the well-studied {\em deletion propagation} problem, the difference being that we are interested in removing the smallest subset of input tuples to remove a given number of output tuples} while deletion propagation focuses on removing a specific output tuple. We call this the {\em Aggregated Deletion Propagation} problem. We completely characterize the poly-time solvability of this problem for arbitrary conjunctive queries without self-joins. This includes a poly-time algorithm to decide solvability, as well as an exact structural characterization of NP-hard instances. We also provide a practical algorithm for this problem (a heuristic for NP-hard instances) and evaluate its experimental performance on real and synthetic datasets.