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Journal Articles Journal of the ACM (JACM) Year : 2022

Enumeration for FO Queries over Nowhere Dense Graphs

Abstract

We consider the evaluation of ÿrst-order queries over classes of databases that are nowhere dense. The notion of nowhere dense classes was introduced by Nešet°il and Ossona de Mendez as a formaliza-tion of classes of “sparse” graphs and generalizes many well-known classes of graphs, such as classes of bounded degree, bounded tree-width, or bounded expansion. It has recently been shown by Grohe, Kreutzer, and Siebertz that over nowhere dense classes of databases, ÿrst-order sentences can be evaluated in pseudo-linear time (pseudo-linear time means that for all  there exists an algorithm working in time O(n1+), where n is the size of the database). For ÿrst-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.
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Dates and versions

hal-03809754 , version 1 (11-10-2022)

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Nicole Schweikardt, Luc Segoufin, Alexandre Vigny. Enumeration for FO Queries over Nowhere Dense Graphs. Journal of the ACM (JACM), 2022, 69 (3), pp.1-37. ⟨10.1145/3517035⟩. ⟨hal-03809754⟩
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