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Abstract not found

In this paper, we address the complexity issue of reasoning with implication constraints. We consider the IC-RFT problem, which is the problem of deciding whether a conjunctive yes/no query always produces the empty relation ("no" answer) on database instances satisfying a given set of implication constraints, as a central problem in this respect. We show that several other important problems, such as the query containment problem, are polynomially equivalent to the IC-RFT problem. More importantly, we give criteria for designing a set of implication constraints so that an efficient "units-refutation" process can be used to solve the IC-RFT problem.

We present a Garey/Johnson-style list of problems known to be complete for the second and higher levels of the polynomial-time Hierarchy (polynomial hierarchy, or PH for short). We also include the best-known hardness of approximation results. The list will be updated as necessary. Updates The compendium currently lists more than 80 problems. Latest changes include: • added [GT26] SUCCINCT k-KING, • added [GT25] SUCCINCT k-DIAMETER, • added [GT4] SUCCINCT k-RADIUS at third level, • added [GT24] MINIMUM VERTEX COLORING DEFINING SET, • added [GT23] GRAPH SANDWICH PROBLEM FOR Π, • added [L24] MINIMUM 3SAT DEFINING SET,

We consider the problem of answering queries using views, where queries and views are conjunctive queries with arithmetic comparisons over dense orders. Previous work only considered limited variants of this problem, without giving a complete solution. We first show that obtaining equivalent rewritings for conjunctive queries with arithmetic comparisons is decidable. Then we consider the problem of finding maximally contained rewritings (MCR) where the decidability proof does not carry over. We investigate two special cases of this problem where the query uses only semi-interval comparisons. In both cases decidability of finding MCRs depends on the query containment test. First, we address the case where the homomorphism property holds in testing query containment. In this case decidability is easy to prove but developing an efficient algorithm is not trivial. We develop such an algorithm and prove that it is sound and complete. This algorithm applies in many cases where the query uses only left (or right) semiinterval comparisons. Then we develop a new query containment test for the case where the containing query uses both left and right semi-interval comparisons but with only one left (or right) semi interval subgoal. Based on this test, we show how to produce an MCR which is a Datalog query with arithmetic comparisons. The containment test that we develop obtains a result of independent interest. It finds another special case where query containment in the presence of arithmetic comparisons can be tested in nondeterministic polynomial time. 1

Query containment is a fundamental algorithmic problem in database query processing and optimization. Under set semantics, the query-containment problem for conjunctive queries has long been known to be NP-complete. In real database systems, however, queries are usually evaluated under bag semantics, not set semantics. In particular, SQL queries are evaluated under bag semantics and return multisets as answers, since duplicates are not eliminated unless explicitly requested. The exact complexity of the query-containment problem for conjunctive queries under bag semantics has been an open problem for more than a decade; in fact, it is not even known whether this problem is decidable. Here, we investigate, under bag semantics, the query-containment problem for conjunctive queries with inequalities. It has been previously shown that, under set semantics, this problem is complete for the second level of the polynomial hierarchy. Our main result asserts that, under bag semantics, the query-containment problem for conjunctive queries with inequalities is undecidable. Actually, we establish the stronger result that this problem is undecidable even if the following two restrictions hold at the same time: (1) the queries use just a single binary relation; and (2) the total number of inequalities is bounded by a certain fixed value. Moreover, the same undecidability results hold under bag-set semantics.

In this paper we present the organization of a predicate-based query cache suitable for integration with agent-based heterogeneous database systems. The cache is managed using a tractable (sound and complete) query containment algorithm, yet there are no language restrictions placed on the applications. This is accomplished by introducing query approximation. Query approximation is a compilation technique where a query expression in a general query language is mapped to a query expression in a restricted language. We define a target language such that query containment can be tested in polynomial time. We define a query approximation method that guarantees that the approximate query contains the original query. In the remainder of the paper we specify the algorithms by which the query engine and the cache manager may negotiate a choice of approximation and the development of a query plan. We use two application workloads and the TPC-D benchmark queries to assess the impact of query app...