Enumeration for FOQueries over Nowhere Dense Graphs
نویسندگان
چکیده
We consider the evaluation of first-order queries over classes of databases that are nowhere dense. The notion of nowhere dense classes was introduced by Nešetřil and Ossona de Mendez as a formalization of classes of “sparse” graphs and generalizes many well-known classes of graphs, such as classes of bounded degree, bounded treewidth, or bounded expansion. It has recently been shown by Grohe, Kreutzer, and Siebertz that over nowhere dense classes of databases, first-order sentences can be evaluated in pseudo-linear time (pseudo-linear time means that for all ε there exists an algorithm working in time O (n1+ε ), where n is the size of the database). For first-order queries of higher arities, we show that over any nowhere dense class of databases, the set of their solutions can be enumerated with constant delay after a pseudo-linear time preprocessing. In the same context, we also show that after a pseudo-linear time preprocessing we can, on input of a tuple, test in constant time whether it is a solution to the query. ACM Reference Format: Nicole Schweikardt, Luc Segoufin, and Alexandre Vigny. 2018. Enumeration for FOQueries over Nowhere Dense Graphs. In PODS’18: 37th ACM SIGMODSIGACT-SIGAI Symposium on Principles of Database Systems, June 10–15, 2018, Houston, TX, USA. ACM, New York, NY, USA, 13 pages. https://doi. org/10.1145/3196959.3196971
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