First-Order Query Evaluation with Cardinality Conditions
Abstract
We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL's COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query evaluation for this logic is fixed-parameter tractable on classes of structures (or databases) of bounded degree. In the present paper, we first show that the fixed-parameter tractability of FOC(P) cannot even be generalised to very simple classes of structures of unbounded degree such as unranked trees or strings with a linear order relation. Then we identify a fragment FOC1(P) of FOC(P) which is still sufficiently strong to express standard applications of SQL's COUNT operator. Our main result shows that query evaluation for FOC1(P) is fixed-parameter tractable with almost linear running time on nowhere dense classes of structures. As a corollary, we also obtain a fixed-parameter tractable algorithm for counting the number of tuples satisfying a query over nowhere dense classes of structures.
Cite
@article{arxiv.1707.05945,
title = {First-Order Query Evaluation with Cardinality Conditions},
author = {Martin Grohe and Nicole Schweikardt},
journal= {arXiv preprint arXiv:1707.05945},
year = {2017}
}