A Unified Approach for Resilience and Causal Responsibility with Integer Linear Programming (ILP) and LP Relaxations

12/17/2022
by   Neha Makhija, et al.
0

Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete from a database in order to remove all answers from a query? A long-open question is determining those conjunctive queries (CQs) for which this problem can be solved in guaranteed PTIME. We shed new light on this and the related problem of causal responsibility by proposing a unified Integer Linear Programming (ILP) formulation. It is unified in that it can solve both prior studied restrictions (e.g., self-join-free CQs under set semantics that allow a PTIME solution) and new cases (e.g., all CQs under set or bag semantics It is also unified in that all queries and all instances are treated with the same approach, and the algorithm is guaranteed to terminate in PTIME for the easy cases. We prove that, for all easy self-join-free CQs, the Linear Programming (LP) relaxation of our encoding is identical to the ILP solution and thus standard ILP solvers are guaranteed to return the solution in PTIME. Our approach opens up the door to new variants and new fine-grained analysis: 1) It also works under bag semantics and we give the first dichotomy result for bags semantics in the problem space. 2) We give a more fine-grained analysis of the complexity of causal responsibility. 3) We recover easy instances for generally hard queries, such as instances with read-once provenance and instances that become easy because of Functional Dependencies in the data. 4) We solve an open conjecture from PODS 2020. 5) Experiments confirm that our results indeed predict the asymptotic running times, and that our universal ILP encoding is at times even faster to solve for the PTIME cases than a prior proposed dedicated flow algorithm.

READ FULL TEXT
research
08/25/2023

Discovering Dichotomies for Problems in Database Theory

Dichotomy theorems, which characterize the conditions under which a prob...
research
05/29/2021

Towards a Dichotomy for Minimally Factorizing the Provenance of Self-Join Free Conjunctive Queries

We consider the problem of finding the minimal-size factorization of the...
research
07/02/2019

New Results for the Complexity of Resilience for Binary Conjunctive Queries with Self-Joins

The resilience of a Boolean query is the minimum number of tuples that n...
research
01/07/2022

Tight Fine-Grained Bounds for Direct Access on Join Queries

We consider the task of lexicographic direct access to query answers. Th...
research
08/16/2021

A scaleable projection-based branch-and-cut algorithm for the p-center problem

The p-center problem (pCP) is a fundamental problem in location science,...
research
06/24/2019

Bag Query Containment and Information Theory

The query containment problem is a fundamental algorithmic problem in da...

Please sign up or login with your details

Forgot password? Click here to reset