Discovering Dichotomies for Problems in Database Theory

TL;DR

This paper introduces a novel approach to discovering dichotomy theorems in database theory, identifying new tractable cases and complexity boundaries for problems like provenance factorization and query resilience under bag semantics.

Contribution

It proposes unified algorithms for classifying problem complexity, leading to new dichotomies and tractability results in reverse data management and knowledge representation.

Findings

New tractable cases for minimal provenance formula factorization

Dichotomies under bag semantics for resilience and causal responsibility

Unified algorithms guarantee PTIME termination for easy cases

Abstract

Dichotomy theorems, which characterize the conditions under which a problem can be solved efficiently, have helped identify important tractability borders for as probabilistic query evaluation, view maintenance, query containment (among many more problems). However, dichotomy theorems for many such problems remain elusive under key settings such as bag semantics or for queries with self-joins. This work aims to unearth dichotomies for fundamental problems in reverse data management and knowledge representation. We use a novel approach to discovering dichotomies: instead of creating dedicated algorithms for easy (PTIME) and hard cases (NP-complete), we devise unified algorithms that are guaranteed to terminate in PTIME for easy cases. Using this approach, we discovered new tractable cases for the problem of minimal factorization of provenance formulas as well as dichotomies under bag semantics for the problems of resilience and causal responsibility