Computing possible and certain answers over order-incomplete data

Amarilli, Antoine; Ba, Mouhamadou Lamine; Deutch, Daniel; Senellart, Pierre

doi:10.1016/j.tcs.2019.05.013

Cited by 5 publications

(6 citation statements)

References 51 publications

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“…We note that a similar task was already known to be in PTIME by [ABDS17,Theorem 17], but showing the space bound given here will introduce several additional technicalities. From Proposition C.2, it is easy to show Proposition 4.5:…”

Section: C3 Proof Of Proposition 45: Tractability Based On Widthmentioning

confidence: 85%

Topological Sorting under Regular Constraints

Amarilli,

Paperman

2017

Preprint

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We introduce the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K. This natural problem applies to several settings, e.g., scheduling with costs or verifying concurrent programs. We consider the problem CTS [K] where the target language K is fixed, and study its complexity depending on K. We show that CTS[K] is tractable when K falls in several language families, e.g., unions of monomials, which can be used for pattern matching. However, we show that CTS[K] is NP-hard for K = (ab) * and introduce a shuffle reduction technique to show hardness for more languages. We also study the special case of the constrained shuffle problem (CSh), where the input graph is a disjoint union of strings, and show that CSh[K] is additionally tractable when K is a group language or a union of district group monomials. We conjecture that a dichotomy should hold on the complexity of CTS[K] or CSh[K] depending on K, and substantiate this by proving a coarser dichotomy under a different problem phrasing which ensures that tractable languages are closed under common operators. ACM Subject Classification Mathematics of computing → Graph algorithmsKeywords and phrases Topological sorting; shuffle problem; regular language Acknowledgements We thank Michaël Cadilhac and Pierre McKenzie for their fruitful insights.

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Section: C3 Proof Of Proposition 45: Tractability Based On Widthmentioning

confidence: 85%

Topological Sorting under Regular Constraints

Amarilli,

Paperman

2017

Preprint

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“…al. extends the relational model with a partial order to encode uncertainty in the sort order of a relation [10,11]. For more general use cases where posets can not represent all possible worlds, Amarilli et.…”

Section: Related Workmentioning

confidence: 99%

“…al. also develop a symbolic model of provenance [9] whose expressions encode possible orders. Both approaches are limited to set semantics.…”

Section: Related Workmentioning

confidence: 99%

Uncertainty Annotated Databases - A Lightweight Approach for Approximating Certain Answers

Huber

Glavic

et al. 2019

Proceedings of the 2019 International Conference on Management of Data

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Certain answers are a principled method for coping with uncertainty that arises in many practical data management tasks. Unfortunately, this method is expensive and may exclude useful (if uncertain) answers. Thus, users frequently resort to less principled approaches to resolve the uncertainty. In this paper, we propose Uncertainty Annotated Databases (UA-DBs), which combine an under-and over-approximation of certain answers to achieve the reliability of certain answers, with the performance of a classical database system. Furthermore, in contrast to prior work on certain answers, UA-DBs achieve a higher utility by including some (explicitly marked) answers that are not certain. UA-DBs are based on incomplete K-relations, which we introduce to generalize the classical set-based notions of incomplete databases and certain answers to a much larger class of data models. Using an implementation of our approach, we demonstrate experimentally that it efficiently produces tight approximations of certain answers that are of high utility.

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Section: :53mentioning

confidence: 99%

“…In the process of preparing a journal version of this paper [ABDS18], we have discovered a flaw in the proof of some of our tractability results on ia-width. We have accordingly removed these results from [ABDS18] and from the present version of this paper. However, the results still survive in the first version of this paper on arXiv [ABDS17b] and in the published version in the TIME proceedings [ABDS17a].…”

Section: :53mentioning

confidence: 99%

Possible and Certain Answers for Queries over Order-Incomplete Data

Amarilli¹,

Ba²,

Deutch³

et al. 2017

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To combine and query ordered data from multiple sources, one needs to handle uncertainty about the possible orderings. Examples of such "order-incomplete" data include integrated event sequences such as log entries; lists of properties (e.g., hotels and restaurants) ranked by an unknown function reflecting relevance or customer ratings; and documents edited concurrently with an uncertain order on edits. This paper introduces a query language for order-incomplete data, based on the positive relational algebra with order-aware accumulation. We use partial orders to represent order-incomplete data, and study possible and certain answers for queries in this context. We show that these problems are respectively NP-complete and coNP-complete, but identify tractable cases depending on the query operators or input partial orders.

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Computing possible and certain answers over order-incomplete data

Cited by 5 publications

References 51 publications

Topological Sorting under Regular Constraints

Topological Sorting under Regular Constraints

Uncertainty Annotated Databases - A Lightweight Approach for Approximating Certain Answers

Possible and Certain Answers for Queries over Order-Incomplete Data

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