arXiv subjects

Neha Makhija

Publications and source records attributed to Neha Makhija.

5 recordsLinked to original sources

arXiv2025

Resilience for Regular Path Queries: Towards a Complexity Classification

The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries (RPQs) over graph databases. Our goal is to characterize the regular languages L for which it is tractable to compute the resilience of the existentially-quantified RPQ built from L. We show that computing the resilience in this sense is tractable (even in combined complexity) for all RPQs defined from so-called local languages. By contrast, we show hardness in data complexity for RPQs defined from the following language classes (after reducing the languages to eliminate redundant words): all finite languages featuring a word containing a repeated letter, and all languages featuring a specific kind of counterexample to being local (which we call four-legged languages). The latter include in particular all languages that are not star-free. Our results also imply hardness for all non-local languages with a so-called neutral letter. We last show tractability for some classes of non-local languages, namely the so-called bipartite chain languages and one-dangling languages, and highlight some remaining obstacles towards a full dichotomy.

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arXiv2025

Is Integer Linear Programming All You Need for Deletion Propagation? A Unified and Practical Approach for Generalized Deletion Propagation

Deletion Propagation (DP) refers to a family of database problems rooted in the classical view-update problem: how to propagate intended deletions in a view (query output) back to the source database while satisfying constraints and minimizing side effects. Although studied for over 40 years, DP variants, their complexities, and practical algorithms have been typically explored in isolation. This work presents a unified and generalized framework for DP with several key benefits: (1) It unifies and generalizes all previously known DP variants, effectively subsuming them within a broader class of problems, including new, well-motivated variants. (2) It comes with a practical and general-purpose algorithm that is ``coarse-grained instance-optimal'': it runs in PTIME for all known PTIME cases and can automatically exploit structural regularities in the data, i.e. it does not rely on hints about such regularities as part of the input. (3) It is complete: our framework handles all known DP variants in all settings (including those involving self-joins, unions, and bag semantics), and allows us to provide new complexity results. (4) It is easy to implement and, in many cases, outperforms prior variant-specific solutions, sometimes by orders of magnitude. We provide the first experimental results for several DP variants previously studied only in theory.

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arXiv2024

Minimally Factorizing the Provenance of Self-join Free Conjunctive Queries

We consider the problem of finding the minimal-size factorization of the provenance of self-join-free conjunctive queries, i.e., we want to find a formula that minimizes the number of variable repetitions. This problem is equivalent to solving the fundamental Boolean formula factorization problem for the restricted setting of the provenance formulas of self-join free queries. While general Boolean formula minimization is $Σ^p_2$-complete, we show that the problem is NP-C in our case. Additionally, we identify a large category of queries that can be solved in PTIME, expanding beyond the previously known tractable cases of read-once formulas and hierarchical queries. We describe connections between factorizations, Variable Elimination Orders (VEOs), and minimal query plans. We leverage these insights to create an Integer Linear Program (ILP) that can solve the minimal factorization problem exactly. We also propose a Max-Flow Min-Cut (MFMC) based algorithm that gives an efficient approximate solution. Importantly, we show that both the Linear Programming (LP) relaxation of our ILP, and our MFMC-based algorithm are always correct for all currently known PTIME cases. Thus, we present two unified algorithms (ILP and MFMC) that can both recover all known PTIME cases in PTIME, yet also solve NP-complete cases either exactly (ILP) or approximately (MFMC), as desired.

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arXiv2023

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

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.

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arXiv2023

Discovering Dichotomies for Problems in Database Theory

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

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