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Asymptotic Determinacy of Path Queries Using Union-of-Paths Views

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Abstract

We consider the view-based query determinacy problem over graph databases for queries defined as unions of path queries. These queries select pairs of nodes in a graph that are connected through a path whose length falls in a given set. A view specification is a set of such queries. We say that a view specification V determines a query Q if, for all databases D, the answers to V on D contain enough information to answer Q. Our main result states that, given a view V, there exists an explicit bound that depends on V such that we can decide the determinacy problem for all queries that ask for a path longer than this bound, and provide first-order rewritings for the queries that are determined. We call this notion asymptotic determinacy. As a corollary, we can also compute the set of almost all path queries that are determined by V.

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Notes

  1. Please note that this definition differs slightly from the definition in [4] in that we did not require in [4] that G had both negative and positive cycles in order to proceed to Step 2. This minor difference does not actually change any of the proofs, as Lemma 6 did not make use of this part of the construction, and Lemma 9 already assumes that the graph contains cycles of both signs. It does however make the size analysis at the end of Section 4.1 (which was not featured in [4]) easier.

  2. If a i = d−1 for some i, then the property of the lemma is falsified by the subsequence a i obtained with j = i.

  3. arbitrarily, when there are more than one possibility.

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Acknowledgments

I gratefully thank Luc Segoufin and Cristina Sirangelo for carefully proofreading this paper and providing many invaluable comments and advices. I also thank the anonymous reviewers for their painstaking and helpful reviews.

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  1. ENS-Cachan, Inria, Cachan, France

    Nadime Francis

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  1. Nadime Francis
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Correspondence to Nadime Francis.

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Part of this work was done while the author was supported by EPSRC grant EP/M025268/1.

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Francis, N. Asymptotic Determinacy of Path Queries Using Union-of-Paths Views. Theory Comput Syst 61, 156–190 (2017). https://doi.org/10.1007/s00224-016-9697-x

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