Tractable counting of the answers to conjunctive queries

Pichler, Reinhard; Skritek, Sebastian

doi:10.1016/j.jcss.2013.01.012

Cited by 42 publications

(73 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Already for acyclic conjunctive queries the combined complexity is #P -complete [25] and only the quantifier free acyclic conjunctive queries can be solved in time linear in ||D|| [3]. Adding just one quantifier already make already the problem hard [26].…”

Section: Counting the Number Of Solutionsmentioning

confidence: 99%

Constant Delay Enumeration for Conjunctive Queries

Segoufin

2015

SIGMOD Rec.

View full text Add to dashboard Cite

We survey some of the recent results about enumerating the answers to queries over a database. We focus on the case where the enumeration is performed with a constant delay between any two consecutive solutions, after a linear time preprocessing.This cannot be always achieved. It requires restricting either the class of queries or the class of databases.We consider conjunctive queries and describe several scenarios when this is possible.

show abstract

Section: Counting the Number Of Solutionsmentioning

confidence: 99%

Constant Delay Enumeration for Conjunctive Queries

Segoufin

2015

SIGMOD Rec.

View full text Add to dashboard Cite

show abstract

“…On bounded-arity queries and if no projection is allowed, counting is known to be tractable over a class C if, and only if, queries in C have bounded treewidth [12,17]-hence, cores play no role here. Moreover, without projections, most commonly considered structural restrictions generalizing acyclicity yield tractable counting problems, even without fixing any arity bound [35]. However, in almost all practical applications, there are variables that are crucial to join different relations in the query, but that are irrelevant to the user, i.e., they are not required in the output and their instantiations must not be counted.…”

Section: Structural Decomposition Methodsmentioning

confidence: 99%

“…• Pichler and Skritek [35] observed that classical decomposition methods are not helpful when projections are allowed. Indeed, they showed that counting answers is #P-hard in this case, even for acyclic queries.…”

Section: Structural Decomposition Methodsmentioning

confidence: 99%

Counting solutions to conjunctive queries

Greco

Scarcello

2014

Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

View full text Add to dashboard Cite

Counting the number of answers to conjunctive queries is an intractable problem, formally #P-hard, even over classes of acyclic queries. However, Durand and Mengel have recently introduced the notion of quantified star size that, combined with hypertree decompositions, identifies islands of tractability for the problem. They also wonder whether such a notion precisely characterizes those classes for which the counting problem is tractable. We show that this is the case only for bounded-arity simple queries, where relation symbols cannot be shared by different query atoms.Indeed, we give a negative answer to the question in the general case, by exhibiting a more powerful structural method based on the novel concept of #-generalized hypertree decomposition. On classes of queries with bounded #-generalized hypertree width, counting answers is shown to be feasible in polynomial time, after a fixed-parameter polynomial-time preprocessing that only depends on the query structure. A weaker variant (but still more general than the technique based on the quantified starsize) is also proposed, for which tractability is established without any exponential dependency on the query size.Based on #-generalized hypertree decompositions, a "hybrid" decomposition method is eventually conceived, where structural properties of the query are exploited in combination with properties of the given database, such as keys or other (weaker) dependencies among attributes that limit the allowed combinations of values. Intuitively, such features may induce different structural properties that are not identified by the "worst-possible database" perspective of purely structural methods.

show abstract

“…The result is also tight on recursively enumerable classes of instances having bounded arity (unless FPT = W [1]) [19]. Moreover, in the general case of classes of instances having bounded hypertree width and with arbitrary sets O of desired variables, the problem is still tractable if either the constraint relations or the constraint scopes have a fixed maximum size [70].…”

Section: Theorem 43 ([48]mentioning

confidence: 99%

Treewidth and Hypertree Width

Gottlob¹,

Greco²,

Scarcello³

2014

Tractability

View full text Add to dashboard Cite

The chapter covers methods for identifying islands of tractability for NP-hard combinatorial problems by exploiting suitable properties of their graphical structure. Acyclic structures are considered, as well as nearly acyclic ones identified by means of so-called structural decomposition methods. In particular, the chapter focuses on the tree decomposition method, which is the most powerful decomposition method for graphs, and on the hypertree decomposition method, which is its natural counterpart for hypergraphs. These problem-decomposition methods give rise to corresponding notions of width of an instance, namely, treewidth and hypertree width. It turns out that many NP-hard problems can be solved efficiently over classes of instances of bounded treewidth or hypertree width: deciding whether a solution exists, computing a solution, and even computing an optimal solution (if some cost function over solutions is specified) are all polynomial-time tasks. Example applications include problems from artificial intelligence, databases, game theory, and combinatorial auctions.

show abstract

Tractable counting of the answers to conjunctive queries

Cited by 42 publications

References 25 publications

Constant Delay Enumeration for Conjunctive Queries

Constant Delay Enumeration for Conjunctive Queries

Counting solutions to conjunctive queries

Treewidth and Hypertree Width

Contact Info

Product

Resources

About