arXiv subjects

Paraschos Koutris

Publications and source records attributed to Paraschos Koutris.

At least 37 records · Page 2Linked to original sources

arXiv2023

Consistent Query Answering for Primary Keys on Rooted Tree Queries

We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal subset of the database satisfying the primary key constraints. For a Boolean query q, the problem CERTAINTY(q) takes a database as input, and asks whether or not each repair satisfies q. The computational complexity of CERTAINTY(q) has been established whenever q is a self-join-free Boolean conjunctive query, or a (not necessarily self-join-free) Boolean path query. In this paper, we take one more step towards a general classification for all Boolean conjunctive queries by considering the class of rooted tree queries. In particular, we show that for every rooted tree query q, CERTAINTY(q) is in FO, NL-hard $\cap$ LFP, or coNP-complete, and it is decidable (in polynomial time), given q, which of the three cases applies. We also extend our classification to larger classes of queries with simple primary keys. Our classification criteria rely on query homomorphisms and our polynomial-time fixpoint algorithm is based on a novel use of context-free grammar (CFG).

cs.DB↗

arXiv2023

Conjunctive Queries with Negation and Aggregation: A Linear Time Characterization

In this paper, we study the complexity of evaluating Conjunctive Queries with negation (\cqneg). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called free-connex signed-acyclic queries. We show that no other queries admit such an algorithm subject to lower bound conjectures. Second, we extend our algorithm to Conjunctive Queries with negation and aggregation over a general semiring, which we call Functional Aggregate Queries with negation (\faqneg). Such an algorithm achieves constant delay enumeration for the same class of queries, but with a slightly increased preprocessing time which includes an inverse Ackermann function. We show that this surprising appearance of the Ackermmann function is probably unavoidable for general semirings, but can be removed when the semiring has specific structure. Finally, we show an application of our results to computing the difference of CQs.

cs.DB↗

arXiv2023

Consistent Query Answering for Primary Keys on Path Queries

We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal consistent subset of the database. For a Boolean query $q$, the problem $\mathsf{CERTAINTY}(q)$ takes a database as input, and asks whether or not each repair satisfies $q$. It is known that for any self-join-free Boolean conjunctive query $q$, $\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$, $\mathbf{LSPACE}$-complete, or $\mathbf{coNP}$-complete. In particular, $\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$ for any self-join-free Boolean path query $q$. In this paper, we show that if self-joins are allowed, the complexity of $\mathsf{CERTAINTY}(q)$ for Boolean path queries $q$ exhibits a tetrachotomy between $\mathbf{FO}$, $\mathbf{NL}$-complete, $\mathbf{PTIME}$-complete, and $\mathbf{coNP}$-complete. Moreover, it is decidable, in polynomial time in the size of the query~$q$, which of the four cases applies.

cs.DB↗

arXiv2023

The Fine-Grained Complexity of CFL Reachability

Many problems in static program analysis can be modeled as the context-free language (CFL) reachability problem on directed labeled graphs. The CFL reachability problem can be generally solved in time $O(n^3)$, where $n$ is the number of vertices in the graph, with some specific cases that can be solved faster. In this work, we ask the following question: given a specific CFL, what is the exact exponent in the monomial of the running time? In other words, for which cases do we have linear, quadratic or cubic algorithms, and are there problems with intermediate runtimes? This question is inspired by recent efforts to classify classic problems in terms of their exact polynomial complexity, known as {\em fine-grained complexity}. Although recent efforts have shown some conditional lower bounds (mostly for the class of combinatorial algorithms), a general picture of the fine-grained complexity landscape for CFL reachability is missing. Our main contribution is lower bound results that pinpoint the exact running time of several classes of CFLs or specific CFLs under widely believed lower bound conjectures (Boolean Matrix Multiplication and $k$-Clique). We particularly focus on the family of Dyck-$k$ languages (which are strings with well-matched parentheses), a fundamental class of CFL reachability problems. We present new lower bounds for the case of sparse input graphs where the number of edges $m$ is the input parameter, a common setting in the database literature. For this setting, we show a cubic lower bound for Andersen's Pointer Analysis which significantly strengthens prior known results.

cs.FL↗

arXiv2023

General Space-Time Tradeoffs via Relational Queries

In this paper, we investigate space-time tradeoffs for answering Boolean conjunctive queries. The goal is to create a data structure in an initial preprocessing phase and use it for answering (multiple) queries. Previous work has developed data structures that trade off space usage for answering time and has proved conditional space lower bounds for queries of practical interest such as the path and triangle query. However, most of these results cater to only those queries, lack a comprehensive framework, and are not generalizable. The isolated treatment of these queries also fails to utilize the connections with extensive research on related problems within the database community. The key insight in this work is to exploit the formalism of relational algebra by casting the problems as answering join queries over a relational database. Using the notion of boolean {\em adorned queries} and {\em access patterns}, we propose a unified framework that captures several widely studied algorithmic problems. Our main contribution is three-fold. First, we present an algorithm that recovers existing space-time tradeoffs for several problems. The algorithm is based on an application of the {\em join size bound} to capture the space usage of our data structure. We combine our data structure with {\em query decomposition} techniques to further improve the tradeoffs and show that it is readily extensible to queries with negation. Second, we falsify two proposed conjectures in the existing literature related to the space-time lower bound for path queries and triangle detection for which we show unexpectedly better algorithms. This result opens a new avenue for improving several algorithmic results that have so far been assumed to be (conditionally) optimal. Finally, we prove new conditional space-time lower bounds for star and path queries.

cs.DS↗

arXiv2023

The Fine-Grained Complexity of Boolean Conjunctive Queries and Sum-Product Problems

We study the fine-grained complexity of evaluating Boolean Conjunctive Queries and their generalization to sum-of-product problems over an arbitrary semiring. For these problems, we present a general semiring-oblivious reduction from the k-clique problem to any query structure (hypergraph). Our reduction uses the notion of embedding a graph to a hypergraph, first introduced by Marx. As a consequence of our reduction, we can show tight conditional lower bounds for many classes of hypergraphs, including cycles, Loomis-Whitney joins, some bipartite graphs, and chordal graphs. These lower bounds have a dependence on what we call the clique embedding power of a hypergraph H, which we believe is a quantity of independent interest. We show that the clique embedding power is always less than the submodular width of the hypergraph, and present a decidable algorithm for computing it. We conclude with many open problems for future research.

cs.DB↗

arXiv2023

Space-Time Tradeoffs for Conjunctive Queries with Access Patterns

In this paper, we investigate space-time tradeoffs for answering conjunctive queries with access patterns (CQAPs). The goal is to create a space-efficient data structure in an initial preprocessing phase and use it for answering (multiple) queries in an online phase. Previous work has developed data structures that trades off space usage for answering time for queries of practical interest, such as the path and triangle query. However, these approaches lack a comprehensive framework and are not generalizable. Our main contribution is a general algorithmic framework for obtaining space-time tradeoffs for any CQAP. Our framework builds upon the $\PANDA$ algorithm and tree decomposition techniques. We demonstrate that our framework captures all state-of-the-art tradeoffs that were independently produced for various queries. Further, we show surprising improvements over the state-of-the-art tradeoffs known in the existing literature for reachability queries.

cs.DB↗

arXiv2022

LinCQA: Faster Consistent Query Answering with Linear Time Guarantees

Most data analytical pipelines often encounter the problem of querying inconsistent data that violate pre-determined integrity constraints. Data cleaning is an extensively studied paradigm that singles out a consistent repair of the inconsistent data. Consistent query answering (CQA) is an alternative approach to data cleaning that asks for all tuples guaranteed to be returned by a given query on all (in most cases, exponentially many) repairs of the inconsistent data. This paper identifies a class of acyclic select-project-join (SPJ) queries for which CQA can be solved via SQL rewriting with a linear time guarantee. Our rewriting method can be viewed as a generalization of Yannakakis's algorithm for acyclic joins to the inconsistent setting. We present LinCQA, a system that can output rewritings in both SQL and non-recursive Datalog rules for every query in this class. We show that LinCQA often outperforms the existing CQA systems on both synthetic and real-world workloads, and in some cases, by orders of magnitude.

cs.DB↗

arXiv2022

Ranked Enumeration of Join Queries with Projections

Join query evaluation with ordering is a fundamental data processing task in relational database management systems. SQL and custom graph query languages such as Cypher offer this functionality by allowing users to specify the order via the ORDER BY clause. In many scenarios, the users also want to see the first $k$ results quickly (expressed by the LIMIT clause), but the value of $k$ is not predetermined as user queries are arriving in an online fashion. Recent work has made considerable progress in identifying optimal algorithms for ranked enumeration of join queries that do not contain any projections. In this paper, we initiate the study of the problem of enumerating results in ranked order for queries with projections. Our main result shows that for any acyclic query, it is possible to obtain a near-linear (in the size of the database) delay algorithm after only a linear time preprocessing step for two important ranking functions: sum and lexicographic ordering. For a practical subset of acyclic queries known as star queries, we show an even stronger result that allows a user to obtain a smooth tradeoff between faster answering time guarantees using more preprocessing time. Our results are also extensible to queries containing cycles and unions. We also perform a comprehensive experimental evaluation to demonstrate that our algorithms, which are simple to implement, improve up to three orders of magnitude in the running time over state-of-the-art algorithms implemented within open-source RDBMS and specialized graph databases.

cs.DB↗

arXiv2022

Certifiable Robustness for Nearest Neighbor Classifiers

ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction of a model is certifiably robust. Given a learning algorithm that produces a classifier and given an example at test time, a classification outcome is certifiably robust if it is predicted by every model trained across all possible worlds (repairs) of the uncertain (inconsistent) dataset. This notion of robustness falls naturally under the framework of certain answers. In this paper, we study the complexity of certifying robustness for a simple but widely deployed classification algorithm, $k$-Nearest Neighbors ($k$-NN). Our main focus is on inconsistent datasets when the integrity constraints are functional dependencies (FDs). For this setting, we establish a dichotomy in the complexity of certifying robustness w.r.t. the set of FDs: the problem either admits a polynomial time algorithm, or it is coNP-hard. Additionally, we exhibit a similar dichotomy for the counting version of the problem, where the goal is to count the number of possible worlds that predict a certain label. As a byproduct of our study, we also establish the complexity of a problem related to finding an optimal subset repair that may be of independent interest.

cs.LG↗

arXiv2021

Comprehensive and Efficient Workload Compression

This work studies the problem of constructing a representative workload from a given input analytical query workload where the former serves as an approximation with guarantees of the latter. We discuss our work in the context of workload analysis and monitoring. As an example, evolving system usage patterns in a database system can cause load imbalance and performance regressions which can be controlled by monitoring system usage patterns, i.e.,~a representative workload, over time. To construct such a workload in a principled manner, we formalize the notions of workload {\em representativity} and {\em coverage}. These metrics capture the intuition that the distribution of features in a compressed workload should match a target distribution, increasing representativity, and include common queries as well as outliers, increasing coverage. We show that solving this problem optimally is NP-hard and present a novel greedy algorithm that provides approximation guarantees. We compare our techniques to established algorithms in this problem space such as sampling and clustering, and demonstrate advantages and key trade-offs of our techniques.

cs.DB↗

arXiv2020

Algorithms for a Topology-aware Massively Parallel Computation Model

Most of the prior work in massively parallel data processing assumes homogeneity, i.e., every computing unit has the same computational capability, and can communicate with every other unit with the same latency and bandwidth. However, this strong assumption of a uniform topology rarely holds in practical settings, where computing units are connected through complex networks. To address this issue, Blanas et al. recently proposed a topology-aware massively parallel computation model that integrates the network structure and heterogeneity in the modeling cost. The network is modeled as a directed graph, where each edge is associated with a cost function that depends on the data transferred between the two endpoints. The computation proceeds in synchronous rounds, and the cost of each round is measured as the maximum cost over all the edges in the network. In this work, we take the first step into investigating three fundamental data processing tasks in this topology-aware parallel model: set intersection, cartesian product, and sorting. We focus on network topologies that are tree topologies, and present both lower bounds, as well as (asymptotically) matching upper bounds. The optimality of our algorithms is with respect to the initial data distribution among the network nodes, instead of assuming worst-case distribution as in previous results. Apart from the theoretical optimality of our results, our protocols are simple, use a constant number of rounds, and we believe can be implemented in practical settings as well.

cs.DB↗

arXiv2020

A Comparative Exploration of ML Techniques for Tuning Query Degree of Parallelism

There is a large body of recent work applying machine learning (ML) techniques to query optimization and query performance prediction in relational database management systems (RDBMSs). However, these works typically ignore the effect of \textit{intra-parallelism} -- a key component used to boost the performance of OLAP queries in practice -- on query performance prediction. In this paper, we take a first step towards filling this gap by studying the problem of \textit{tuning the degree of parallelism (DOP) via ML techniques} in Microsoft SQL Server, a popular commercial RDBMS that allows an individual query to execute using multiple cores. In our study, we cast the problem of DOP tuning as a {\em regression} task, and examine how several popular ML models can help with query performance prediction in a multi-core setting. We explore the design space and perform an extensive experimental study comparing different models against a list of performance metrics, testing how well they generalize in different settings: $(i)$ to queries from the same template, $(ii)$ to queries from a new template, $(iii)$ to instances of different scale, and $(iv)$ to different instances and queries. Our experimental results show that a simple featurization of the input query plan that ignores cost model estimations can accurately predict query performance, capture the speedup trend with respect to the available parallelism, as well as help with automatically choosing an optimal per-query DOP.

cs.DB↗

arXiv2019

Scalable inference of topic evolution via models for latent geometric structures

We develop new models and algorithms for learning the temporal dynamics of the topic polytopes and related geometric objects that arise in topic model based inference. Our model is nonparametric Bayesian and the corresponding inference algorithm is able to discover new topics as the time progresses. By exploiting the connection between the modeling of topic polytope evolution, Beta-Bernoulli process and the Hungarian matching algorithm, our method is shown to be several orders of magnitude faster than existing topic modeling approaches, as demonstrated by experiments working with several million documents in under two dozens of minutes.

stat.ML↗

arXiv2019

Revenue Maximization for Query Pricing

Buying and selling of data online has increased substantially over the last few years. Several frameworks have already been proposed that study query pricing in theory and practice. The key guiding principle in these works is the notion of {\em arbitrage-freeness} where the broker can set different prices for different queries made to the dataset, but must ensure that the pricing function does not provide the buyers with opportunities for arbitrage. However, little is known about revenue maximization aspect of query pricing. In this paper, we study the problem faced by a broker selling access to data with the goal of maximizing her revenue. We show that this problem can be formulated as a revenue maximization problem with single-minded buyers and unlimited supply, for which several approximation algorithms are known. We perform an extensive empirical evaluation of the performance of several pricing algorithms for the query pricing problem on real-world instances. In addition to previously known approximation algorithms, we propose several new heuristics and analyze them both theoretically and experimentally. Our experiments show that algorithms with the best theoretical bounds are not necessarily the best empirically. We identify algorithms and heuristics that are both fast and also provide consistently good performance when valuations are drawn from a variety of distributions.

cs.DB↗

arXiv2018

Scaling-Up In-Memory Datalog Processing: Observations and Techniques

Recursive query processing has experienced a recent resurgence, as a result of its use in many modern application domains, including data integration, graph analytics, security, program analysis, networking and decision making. Due to the large volumes of data being processed, several research efforts, across multiple communities, have explored how to scale up recursive queries, typically expressed in Datalog. Our experience with these tools indicated that their performance does not translate across domains (e.g., a tool design for large-scale graph analytics does not exhibit the same performance on program-analysis tasks, and vice versa). As a result, we designed and implemented a general-purpose Datalog engine, called RecStep, on top of a parallel single-node relational system. In this paper, we outline the different techniques we use in RecStep, and the contribution of each technique to overall performance. We also present results from a detailed set of experiments comparing RecStep with a number of other Datalog systems using both graph analytics and program-analysis tasks, summarizing pros and cons of existing techniques based on the analysis of our observations. We show that RecStep generally outperforms the state-of-the-art parallel Datalog engines on complex and large-scale Datalog program evaluation, by a 4-6X margin. An additional insight from our work is that we show that it is possible to build a high-performance Datalog system on top of a relational engine, an idea that has been dismissed in past work in this area.

cs.DB↗

arXiv2018

Consistent Query Answering for Primary Keys in Logspace

We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In [KW17], the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this paper, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.

cs.DB↗

arXiv2018

The Effect of Network Width on the Performance of Large-batch Training

Distributed implementations of mini-batch stochastic gradient descent (SGD) suffer from communication overheads, attributed to the high frequency of gradient updates inherent in small-batch training. Training with large batches can reduce these overheads; however, large batches can affect the convergence properties and generalization performance of SGD. In this work, we take a first step towards analyzing how the structure (width and depth) of a neural network affects the performance of large-batch training. We present new theoretical results which suggest that--for a fixed number of parameters--wider networks are more amenable to fast large-batch training compared to deeper ones. We provide extensive experiments on residual and fully-connected neural networks which suggest that wider networks can be trained using larger batches without incurring a convergence slow-down, unlike their deeper variants.

stat.ML↗