Relative expressive power of navigational querying on graphs

Authors:
George H. L. Fletcher;Marc Gyssens;Dirk Leinders;Jan Van den Bussche;Dirk Van Gucht;Stijn Vansummeren;Yuqing Wu
Affiliations:
Eindhoven University of Technology;Hasselt University & Transnational Univ. of Limburg;Hasselt University & Transnational Univ. of Limburg;Hasselt University & Transnational Univ. of Limburg;Indiana University;Université Libre de Bruxelles;Indiana University
Venue:
Proceedings of the 14th International Conference on Database Theory
Year:
2011

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Abstract

Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; transitive closure; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages. We do this not only for general path queries (queries where the result may be any binary relation) but also for boolean or yes/no queries (expressed by the nonemptiness of an expression). For both cases, we present the complete Hasse diagram of relative expressiveness. In particular, the Hasse diagram for boolean queries contains nontrivial separations and a few surprising collapses.