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Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the application, but typically involves either a lexicographic order (e.g., ORDER BY R.A, S.B in SQL) or a weighted sum of attributes (e.g., ORDER BY 3*R.A + 2*S.B). Recent work has introduced any-k algorithms for (multi-way) join queries, which push ranking into joins and avoid materializing intermediate results until necessary. The top-ranked answers are returned asymptotically faster than the common join-then-rank approach of database systems, resulting in orders-of-magnitude speedup in practice.
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Querying for Queries: Indexes of Queries for Efficient and Expressive IT-PIR
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Given a self-join-free conjunctive queryQand a set of tuplesS, asynthetic witness Dis a database instance such that the result ofQonDisS. In this work, we are interested in two problems. First, the existence problem ESW decides whether any synthetic witnessDexists. Second, given that a synthetic witness exists, the minimization problem SSW computes a synthetic witness of minimal size. The SSW problem is related to thesmallest witness problemrecently studied by Hu and Sintos [22]; however, the objective and the results are inherently different. More specifically, we show that SSW is poly-time solvable for a wider range of queries. Interestingly, in some cases, SSW is related to optimization problems in other domains, such as therole miningproblem in data mining and theedge concentrationproblem in graph drawing. Solutions to ESW and SSW are of practical interest, e.g., fortest database generationfor applications accessing a database and fordata compressionby encoding a datasetSas a pair of a queryQand databaseD. We prove that ESW is in P, presenting a simple algorithm that, given anyS, decides whether a synthetic witness exists in polynomial time in the size ofS. Next, we focus on the SSW problem. We show an algorithm that computes a minimal synthetic witness in polynomial time with respect to the size ofSfor any queryQthat has thehead-dominationproperty. IfQdoes not have such a property, then SSW is generally hard. More specifically, we show that for the class ofpath queries(of any constant length), SSW cannot be solved in polynomial time unless P = NP. We then extend this hardness result to the class ofBerge-acyclicqueries that do not have the head-domination property, obtaining a full dichotomy of SSW for Berge-acyclic queries. Finally, we investigate the hardness of SSW beyond Berge-acyclic queries by showing that SSW cannot be solved in polynomial time for some cyclic queries unless P = NP.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3133956.3134008
