Structurally Tractable Uncertain Data

Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query possibility, certainty, or probability: these problems are hard on arbitrary uncertain input instances. We thus ask whether we could restrict the structure of uncertain data so as to guarantee the tractability of exact query evaluation. We present our tractability results for tree and tree-like uncertain data, and a vision for probabilistic rule reasoning. We also study uncertainty about order, proposing a suitable representation, and study uncertain data conditioned by additional observations.Comment: 11 pages, 1 figure, 1 table. To appear in SIGMOD/PODS PhD Symposium 201

Pure Nash Equilibria: Hard and Easy Games

We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each players payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems

A Trichotomy for Regular Simple Path Queries on Graphs

Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regular simple path queries (RSPQs) find several applications in practice, yet they quickly become intractable, even for basic languages such as (aa)* or a*ba*. In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify the fragment that is maximal in the following sense: regular simple path queries can be evaluated in polynomial time for every regular language L that belongs to this fragment and evaluation is NP-complete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: Evaluations of RSPQs is either AC0, NL-complete or NP-complete in data complexity, depending on the regular language L. The fragment identified also admits a simple characterization in terms of regular expressions. Finally, we also discuss the complexity of the following decision problem: decide, given a language L, whether finding a regular simple path for L is tractable. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NL-complete for the first representation and PSPACE-complete for the other two. As a conclusion we extend our results from edge-labeled graphs to vertex-labeled graphs and vertex-edge labeled graphs.Comment: 15 pages, conference submissio

Beyond Worst-Case Analysis for Joins with Minesweeper

We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is developing a framework to measure this stronger notion of complexity, which we call {\it certificate complexity}, that extends notions of Barbay et al. and Demaine et al.; a certificate is a set of propositional formulae that certifies that the output is correct. This notion captures a natural class of join algorithms. In addition, the certificate allows us to define a strictly stronger notion of runtime complexity than traditional worst-case guarantees. Our second contribution is to develop a dichotomy theorem for the certificate-based notion of complexity. Roughly, we show that Minesweeper evaluates $\beta$-acyclic queries in time linear in the certificate plus the output size, while for any $\beta$-cyclic query there is some instance that takes superlinear time in the certificate (and for which the output is no larger than the certificate size). We also extend our certificate-complexity analysis to queries with bounded treewidth and the triangle query.Comment: [This is the full version of our PODS'2014 paper.

Provenance Circuits for Trees and Treelike Instances (Extended Version)

Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such as counting query results [3] or performing query evaluation on probabilistic trees [10]. These are two examples of the more general problem of computing augmented query output, that is referred to as provenance. This article presents a provenance framework for trees and treelike instances, by describing a linear-time construction of a circuit provenance representation for MSO queries. We show how this provenance can be connected to the usual definitions of semiring provenance on relational instances [20], even though we compute it in an unusual way, using tree automata; we do so via intrinsic definitions of provenance for general semirings, independent of the operational details of query evaluation. We show applications of this provenance to capture existing counting and probabilistic results on trees and treelike instances, and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1

Query-Answer Causality in Databases: Abductive Diagnosis and View-Updates

Causality has been recently introduced in databases, to model, characterize and possibly compute causes for query results (answers). Connections between query causality and consistency-based diagnosis and database repairs (wrt. integrity constrain violations) have been established in the literature. In this work we establish connections between query causality and abductive diagnosis and the view-update problem. The unveiled relationships allow us to obtain new complexity results for query causality -the main focus of our work- and also for the two other areas.Comment: To appear in Proc. UAI Causal Inference Workshop, 2015. One example was fixe

Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2^n) and compute the fractional hypertree-width of H in time O(m*1.734601^n).Comment: 12 pages, 1 figur