Answering aggregate queries in data exchange

Afrati, F; Kolaitis, PG

dc.contributor.author	Afrati, F	en
dc.contributor.author	Kolaitis, PG	en
dc.date.accessioned	2014-03-01T02:45:07Z
dc.date.available	2014-03-01T02:45:07Z
dc.date.issued	2008	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32161
dc.subject	Aggregate queries	en
dc.subject	Data exchange	en
dc.subject	Schema mapping	en
dc.subject.other	Aggregate queries	en
dc.subject.other	Aggregation queries	en
dc.subject.other	Average operators	en
dc.subject.other	Certain answers	en
dc.subject.other	Closed world assumptions	en
dc.subject.other	Complete problems	en
dc.subject.other	Data exchange	en
dc.subject.other	Data exchanges	en
dc.subject.other	Data translations	en
dc.subject.other	First orders	en
dc.subject.other	Incomplete informations	en
dc.subject.other	Lower bounds	en
dc.subject.other	Possible worlds	en
dc.subject.other	Relational schemas	en
dc.subject.other	Schema mapping	en
dc.subject.other	Schema mappings	en
dc.subject.other	Systematic investigations	en
dc.subject.other	Technical contributions	en
dc.subject.other	Time algorithms	en
dc.subject.other	Universal solutions	en
dc.subject.other	Upper bounds	en
dc.subject.other	Agglomeration	en
dc.subject.other	Aggregates	en
dc.subject.other	Control theory	en
dc.subject.other	Data acquisition	en
dc.subject.other	Information theory	en
dc.subject.other	Semantics	en
dc.subject.other	Database systems	en
dc.title	Answering aggregate queries in data exchange	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1145/1376916.1376936	en
heal.identifier.secondary	http://dx.doi.org/10.1145/1376916.1376936	en
heal.publicationDate	2008	en
heal.abstract	Data exchange, also known as data translation, has been extensively investigated in recent years. One main direction of research has focused on the semantics and the complexity of answering first-order queries in the context of data exchange between relational schemas. In this paper, we initiate a systematic investigation of the semantics and the complexity of aggregate queries in data exchange, and make a number of conceptual and technical contributions. Data exchange is a context in which incomplete information arises, hence one has to cope with a set of possible worlds, instead of a single database. Three different sets of possible worlds have been explored in the study of the certain answers of first-order queries in data exchange: the set of possible worlds of all solutions, the set of possible worlds of all universal solutions, and a set of possible worlds derived from the CWA-solutions. We examine each of these sets and point out that none of them is suitable for aggregation in data exchange, as each gives rise to rather trivial semantics. Our analysis also reveals that, to have meaningful semantics for aggregation in data exchange, a strict closed world assumption has to be adopted in selecting the set of possible worlds. For this, we introduce and study the set of the endomorphic images of the canonical universal solution as a set of possible worlds for aggregation in data exchange. Our main technical result is that for schema mappings specified by source-to-target tgds, there are polynomial-time algorithms for computing the range semantics of every scalar aggregation query, where the range semantics of an aggregate query is the greatest lower bound and the least upper bound of the values that the query takes over the set of possible worlds. Among these algorithms, the more sophisticated one is the algorithm for the average operator, which makes use of concepts originally introduced in the study of the core of the universal solutions in data exchange. We also show that if, instead of range semantics, we consider possible answer semantics, then it is an NP-complete problem to tell if a number is a possible answer of a given scalar aggregation query with the average operator. Copyright 2008 ACM.	en
heal.journalName	Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems	en
dc.identifier.doi	10.1145/1376916.1376936	en
dc.identifier.spage	129	en
dc.identifier.epage	138	en