Unlike a reporting query that returns all the elements satisfying a predicate, query sampling returns only a sample set of those elements and has long been recognized as an important method in database systems. PODS'14 saw the introduction of independent query sampling (IQS), which extends traditional query sampling with the requirement that the sample outputs of all the queries be mutually independent. The new requirement improves the precision of query estimation, facilitates the execution of randomized algorithms, and enhances the fairness and diversity of query answers. IQS calls for new index structures because conventional indexes are designed to report complete query answers and thus becomes too expensive for extracting only a few random samples. The phenomenon has created an exciting opportunity to revisit the structure for every reporting query known in computer science. There has been considerable progress since 2014 in this direction. This paper distills the existing solutions into several generic techniques that, when put together, can be utilized to solve a great variety of IQS problems with attractive performance guarantees.
{"title":"Algorithmic Techniques for Independent Query Sampling","authors":"Yufei Tao","doi":"10.1145/3517804.3526068","DOIUrl":"https://doi.org/10.1145/3517804.3526068","url":null,"abstract":"Unlike a reporting query that returns all the elements satisfying a predicate, query sampling returns only a sample set of those elements and has long been recognized as an important method in database systems. PODS'14 saw the introduction of independent query sampling (IQS), which extends traditional query sampling with the requirement that the sample outputs of all the queries be mutually independent. The new requirement improves the precision of query estimation, facilitates the execution of randomized algorithms, and enhances the fairness and diversity of query answers. IQS calls for new index structures because conventional indexes are designed to report complete query answers and thus becomes too expensive for extracting only a few random samples. The phenomenon has created an exciting opportunity to revisit the structure for every reporting query known in computer science. There has been considerable progress since 2014 in this direction. This paper distills the existing solutions into several generic techniques that, when put together, can be utilized to solve a great variety of IQS problems with attractive performance guarantees.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124083055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The information extraction framework of document spanners was introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, J. ACM 2015) as a formalisation of the query language AQL, which is used in IBM's information extraction engine SystemT. Since 2013, this framework has been investigated in depth by the principles of database management community and beyond. The present paper gives a brief overview of concepts, results, and recent developments concerning document spanners.
文档扳手的信息提取框架是由Fagin, Kimelfeld, Reiss和Vansummeren (PODS 2013, J. ACM 2015)作为IBM信息提取引擎SystemT中使用的查询语言AQL的形式化引入的。自2013年以来，这个框架已经被数据库管理社区的原则和其他人深入研究。本文简要概述了有关文档生成器的概念、结果和最新发展。
{"title":"Document Spanners - A Brief Overview of Concepts, Results, and Recent Developments","authors":"Markus L. Schmid, Nicole Schweikardt","doi":"10.1145/3517804.3526069","DOIUrl":"https://doi.org/10.1145/3517804.3526069","url":null,"abstract":"The information extraction framework of document spanners was introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, J. ACM 2015) as a formalisation of the query language AQL, which is used in IBM's information extraction engine SystemT. Since 2013, this framework has been investigated in depth by the principles of database management community and beyond. The present paper gives a brief overview of concepts, results, and recent developments concerning document spanners.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124261878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kuldeep S. Meel, Sourav Chakraborty, N. V. Vinodchandran
Given a family of sets (S1, S2,... SM) over a universe Ω, estimating the size of their union in the data streaming model is a fundamental computational problem with a wide variety of applications. The holy grail in the field of streaming is to seek design of algorithms that achieve (ε, δ)-approximation with poly(log |Ω|, ε-1, log δ-1) space and update time complexity. Earlier investigations achieve algorithms with desired space and update time complexity for restricted cases such as singletons (Distinct Elements problem), one-dimensional ranges, arithmetic progressions, and sub-cubes. However, techniques used in these works fail for many other simple structured sets. A prominent example is that of Klee's Measure Problem (KMP), wherein every set Si is represented by an axis-parallel rectangle in d-dimensional spaces. Despite extensive prior work, the best-known streaming algorithms for many of these cases depend on the size of the stream, and therefore the problem of whether there exists a streaming algorithm for estimations of size of the union of sets with poly(log |Ω|, ε-1, log δ-1) space and update time complexity has remained open. In this work, we focus on certain general families of sets called Delphic families (which allows efficient membership, sampling, and cardinality queries). Such families of sets capture several well-known problems, including KMP, test coverage, and hypervolume estimation. The primary contribution of our work is to resolve the above-mentioned open problem for streams over Delphic families. In particular, we design the first streaming algorithm for estimating |⋃i=1M Si| with poly(log |Ω|, ε-1, log δ-1) space and update time complexity (independent of M, the length of the stream) when each Si is a member from a Delphic family of sets. We further generalize our results to larger families of sets, called approximate-Delphic families, for which the size of a set can be known approximately but not exactly. Our results resolve two of the open problems listed in Meel, Vinodchandran, Chakraborty (PODS-21).
{"title":"Estimation of the Size of Union of Delphic Sets: Achieving Independence from Stream Size","authors":"Kuldeep S. Meel, Sourav Chakraborty, N. V. Vinodchandran","doi":"10.1145/3517804.3526222","DOIUrl":"https://doi.org/10.1145/3517804.3526222","url":null,"abstract":"Given a family of sets (S1, S2,... SM) over a universe Ω, estimating the size of their union in the data streaming model is a fundamental computational problem with a wide variety of applications. The holy grail in the field of streaming is to seek design of algorithms that achieve (ε, δ)-approximation with poly(log |Ω|, ε-1, log δ-1) space and update time complexity. Earlier investigations achieve algorithms with desired space and update time complexity for restricted cases such as singletons (Distinct Elements problem), one-dimensional ranges, arithmetic progressions, and sub-cubes. However, techniques used in these works fail for many other simple structured sets. A prominent example is that of Klee's Measure Problem (KMP), wherein every set Si is represented by an axis-parallel rectangle in d-dimensional spaces. Despite extensive prior work, the best-known streaming algorithms for many of these cases depend on the size of the stream, and therefore the problem of whether there exists a streaming algorithm for estimations of size of the union of sets with poly(log |Ω|, ε-1, log δ-1) space and update time complexity has remained open. In this work, we focus on certain general families of sets called Delphic families (which allows efficient membership, sampling, and cardinality queries). Such families of sets capture several well-known problems, including KMP, test coverage, and hypervolume estimation. The primary contribution of our work is to resolve the above-mentioned open problem for streams over Delphic families. In particular, we design the first streaming algorithm for estimating |⋃i=1M Si| with poly(log |Ω|, ε-1, log δ-1) space and update time complexity (independent of M, the length of the stream) when each Si is a member from a Delphic family of sets. We further generalize our results to larger families of sets, called approximate-Delphic families, for which the size of a set can be known approximately but not exactly. Our results resolve two of the open problems listed in Meel, Vinodchandran, Chakraborty (PODS-21).","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122764242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fundamental research on data manipulation languages is often motivated by the search for balance between desirable properties, such as expressiveness, robustness, compositionality, the existence of efficient algorithms, etc. Real-world data can be helpful for this search in many different respects. Data sets may exhibit common structures that efficient algorithms can exploit. Query logs and schemas can give us an idea of single features that are used very often, or groups of features that are frequently used together. In this sense, they can guide us towards features or fragments of data manipulation languages that are common in practice and may therefore be worthy of deeper study. In other cases, we may even get a glimpse on features that are not well-understood by users, which may inspire us to redesign them or develop tools that increase their ease-of-use. This tutorial aims to provide, first of all, an overview on several practical studies that have been conducted in the areas of tree-structured and graph-structured data, with a focus on cases with strong interaction between analysis of the data and fundamental research. Second, it aims to provide a set of lessons learned after the investigation of some large-scale logs consisting of more than 850 million queries.
{"title":"Towards Theory for Real-World Data","authors":"W. Martens","doi":"10.1145/3517804.3526066","DOIUrl":"https://doi.org/10.1145/3517804.3526066","url":null,"abstract":"Fundamental research on data manipulation languages is often motivated by the search for balance between desirable properties, such as expressiveness, robustness, compositionality, the existence of efficient algorithms, etc. Real-world data can be helpful for this search in many different respects. Data sets may exhibit common structures that efficient algorithms can exploit. Query logs and schemas can give us an idea of single features that are used very often, or groups of features that are frequently used together. In this sense, they can guide us towards features or fragments of data manipulation languages that are common in practice and may therefore be worthy of deeper study. In other cases, we may even get a glimpse on features that are not well-understood by users, which may inspire us to redesign them or develop tools that increase their ease-of-use. This tutorial aims to provide, first of all, an overview on several practical studies that have been conducted in the areas of tree-structured and graph-structured data, with a focus on cases with strong interaction between analysis of the data and fundamental research. Second, it aims to provide a set of lessons learned after the investigation of some large-scale logs consisting of more than 850 million queries.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132284083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Calautti, Ester Livshits, Andreas Pieris, Markus Schneider
Operational consistent query answering (CQA) is a recent framework for CQA, based on revised definitions of repairs and consistent answers, which opens up the possibility of efficient approximations with explicit error guarantees. The main idea is to iteratively apply operations (e.g., fact deletions), starting from an inconsistent database, until we reach a database that is consistent w.r.t. the given set of constraints. This gives us the flexibility of choosing the probability with which we apply an operation, which in turn allows us to calculate the probability of an operational repair, and thus, the probability with which a consistent answer is entailed. A natural way of assigning probabilities to operations is by targeting the uniform probability distribution over a reasonable space such as the set of operational repairs, the set of sequences of operations that lead to an operational repair, and the set of available operations at a certain step of the repairing process. This leads to what we generally call uniform operational CQA. The goal of this work is to perform a data complexity analysis of both exact and approximate uniform operational CQA, focusing on functional dependencies (and subclasses thereof), and conjunctive queries. The main outcome of our analysis (among other positive and negative results), is that uniform operational CQA pushes the efficiency boundaries further by ensuring the existence of efficient approximation schemes in scenarios that go beyond the simple case of primary keys, which seems to be the limit of the classical approach to CQA.
{"title":"Uniform Operational Consistent Query Answering","authors":"M. Calautti, Ester Livshits, Andreas Pieris, Markus Schneider","doi":"10.1145/3517804.3526230","DOIUrl":"https://doi.org/10.1145/3517804.3526230","url":null,"abstract":"Operational consistent query answering (CQA) is a recent framework for CQA, based on revised definitions of repairs and consistent answers, which opens up the possibility of efficient approximations with explicit error guarantees. The main idea is to iteratively apply operations (e.g., fact deletions), starting from an inconsistent database, until we reach a database that is consistent w.r.t. the given set of constraints. This gives us the flexibility of choosing the probability with which we apply an operation, which in turn allows us to calculate the probability of an operational repair, and thus, the probability with which a consistent answer is entailed. A natural way of assigning probabilities to operations is by targeting the uniform probability distribution over a reasonable space such as the set of operational repairs, the set of sequences of operations that lead to an operational repair, and the set of available operations at a certain step of the repairing process. This leads to what we generally call uniform operational CQA. The goal of this work is to perform a data complexity analysis of both exact and approximate uniform operational CQA, focusing on functional dependencies (and subclasses thereof), and conjunctive queries. The main outcome of our analysis (among other positive and negative results), is that uniform operational CQA pushes the efficiency boundaries further by ensuring the existence of efficient approximation schemes in scenarios that go beyond the simple case of primary keys, which seems to be the limit of the classical approach to CQA.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"14 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116647109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The chase procedure, originally introduced for checking implication of database constraints, and later on used for computing data exchange solutions, has recently become a central algorithmic tool in rule-based ontological reasoning. In this context, a key problem is non-uniform chase termination: does the chase of a database w.r.t. a rule-based ontology terminate? And if this is the case, what is the size of the result of the chase? We focus on guarded tuple-generating dependencies (TGDs), which form a robust rule-based ontology language, and study the above central questions for the semi-oblivious version of the chase. One of our main findings is that non-uniform semi-oblivious chase termination for guarded TGDs is feasible in polynomial time w.r.t. the database, and the size of the result of the chase (whenever is finite) is linear w.r.t. the database. Towards our results concerning non-uniform chase termination, we show that basic techniques such as simplification and linearization, originally introduced in the context of ontological query answering, can be safely applied to the chase termination problem.
{"title":"Non-Uniformly Terminating Chase: Size and Complexity","authors":"M. Calautti, G. Gottlob, Andreas Pieris","doi":"10.1145/3517804.3524146","DOIUrl":"https://doi.org/10.1145/3517804.3524146","url":null,"abstract":"The chase procedure, originally introduced for checking implication of database constraints, and later on used for computing data exchange solutions, has recently become a central algorithmic tool in rule-based ontological reasoning. In this context, a key problem is non-uniform chase termination: does the chase of a database w.r.t. a rule-based ontology terminate? And if this is the case, what is the size of the result of the chase? We focus on guarded tuple-generating dependencies (TGDs), which form a robust rule-based ontology language, and study the above central questions for the semi-oblivious version of the chase. One of our main findings is that non-uniform semi-oblivious chase termination for guarded TGDs is feasible in polynomial time w.r.t. the database, and the size of the result of the chase (whenever is finite) is linear w.r.t. the database. Towards our results concerning non-uniform chase termination, we show that basic techniques such as simplification and linearization, originally introduced in the context of ontological query answering, can be safely applied to the chase termination problem.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"360 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117079611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Ajtai, V. Braverman, T. S. Jayram, Sandeep Silwal, Alec Sun, David P. Woodruff, Samson Zhou
There has been a flurry of recent literature studying streaming algorithms for which the input stream is chosen adaptively by a black-box adversary who observes the output of the streaming algorithm at each time step. However, these algorithms fail when the adversary has access to the internal state of the algorithm, rather than just the output of the algorithm. We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still possible. We first give a randomized algorithm for the L1-heavy hitters problem that outperforms the optimal deterministic Misra-Gries algorithm on long streams. If the white-box adversary is computationally bounded, we use cryptographic techniques to reduce the memory of our L1-heavy hitters algorithm even further and to design a number of additional algorithms for graph, string, and linear algebra problems. The existence of such algorithms is surprising, as the streaming algorithm does not even have a secret key in this model, i.e., its state is entirely known to the adversary. One algorithm we design is for estimating the number of distinct elements in a stream with insertions and deletions achieving a multiplicative approximation and sublinear space; such an algorithm is impossible for deterministic algorithms. We also give a general technique that translates any two-player deterministic communication lower bound to a lower bound for randomized algorithms robust to a white-box adversary. In particular, our results show that for all p≥0, there exists a constant Cp>1 such that any Cp-approximation algorithm for Fp moment estimation in insertion-only streams with a white-box adversary requires Ω(n) space for a universe of size n. Similarly, there is a constant C>1 such that any C-approximation algorithm in an insertion-only stream for matrix rank requires Ω(n) space with a white-box adversary. These results do not contradict our upper bounds since they assume the adversary has unbounded computational power. Our algorithmic results based on cryptography thus show a separation between computationally bounded and unbounded adversaries. Finally, we prove a lower bound of Ω(log(n)) bits for the fundamental problem of deterministic approximate counting in a stream of 0s and 1s, which holds even if we know how many total stream updates we have seen so far at each point in the stream. Such a lower bound for approximate counting with additional information was previously unknown, and in our context, it shows a separation between multiplayer deterministic maximum communication and the white-box space complexity of a streaming algorithm.
{"title":"The White-Box Adversarial Data Stream Model","authors":"M. Ajtai, V. Braverman, T. S. Jayram, Sandeep Silwal, Alec Sun, David P. Woodruff, Samson Zhou","doi":"10.1145/3517804.3526228","DOIUrl":"https://doi.org/10.1145/3517804.3526228","url":null,"abstract":"There has been a flurry of recent literature studying streaming algorithms for which the input stream is chosen adaptively by a black-box adversary who observes the output of the streaming algorithm at each time step. However, these algorithms fail when the adversary has access to the internal state of the algorithm, rather than just the output of the algorithm. We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still possible. We first give a randomized algorithm for the L1-heavy hitters problem that outperforms the optimal deterministic Misra-Gries algorithm on long streams. If the white-box adversary is computationally bounded, we use cryptographic techniques to reduce the memory of our L1-heavy hitters algorithm even further and to design a number of additional algorithms for graph, string, and linear algebra problems. The existence of such algorithms is surprising, as the streaming algorithm does not even have a secret key in this model, i.e., its state is entirely known to the adversary. One algorithm we design is for estimating the number of distinct elements in a stream with insertions and deletions achieving a multiplicative approximation and sublinear space; such an algorithm is impossible for deterministic algorithms. We also give a general technique that translates any two-player deterministic communication lower bound to a lower bound for randomized algorithms robust to a white-box adversary. In particular, our results show that for all p≥0, there exists a constant Cp>1 such that any Cp-approximation algorithm for Fp moment estimation in insertion-only streams with a white-box adversary requires Ω(n) space for a universe of size n. Similarly, there is a constant C>1 such that any C-approximation algorithm in an insertion-only stream for matrix rank requires Ω(n) space with a white-box adversary. These results do not contradict our upper bounds since they assume the adversary has unbounded computational power. Our algorithmic results based on cryptography thus show a separation between computationally bounded and unbounded adversaries. Finally, we prove a lower bound of Ω(log(n)) bits for the fundamental problem of deterministic approximate counting in a stream of 0s and 1s, which holds even if we know how many total stream updates we have seen so far at each point in the stream. Such a lower bound for approximate counting with additional information was previously unknown, and in our context, it shows a separation between multiplayer deterministic maximum communication and the white-box space complexity of a streaming algorithm.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117325517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Estimating the number of subgraphs in data streams is a fundamental problem that has received great attention in the past decade. In this paper, we give improved streaming algorithms for approximately counting the number of occurrences of an arbitrary subgraph H, denoted #H, when the input graph G is represented as a stream of m edges. To obtain our algorithms, we provide a generic transformation that converts constant-round sublinear-time graph algorithms in the query access model to constant-pass sublinear-space graph streaming algorithms. Using this transformation, we obtain the following results. • We give a 3-pass turnstile streaming algorithm for (1 ± ε)-approximating #H in Õ(mρ(H) /ε2⋅#H) space, where ρ(H) is the fractional edge-cover of H. This improves upon and generalizes a result of McGregor et al. [PODS 2016], who gave a 3-pass insertion-only streaming algorithm for (1 ± ε)-approximating the number #T of triangles in Õ(m3/2/ε2 ⋅ #T) space if the algorithm is given additional oracle access to the degrees.• We provide a constant-pass streaming algorithm for (1 ± ε)-approximating #Kr in Õ(m/λr-2 ε2 ⋅ #Kr) space for any r ≥ 3, in a graph G with degeneracy λ, where Kr is a clique on r vertices. This resolves a conjecture by Bera and Seshadhri [PODS 2020]. More generally, our reduction relates the adaptivity of a query algorithm to the pass complexity of a corresponding streaming algorithm, and it is applicable to all algorithms in standard sublinear-time graph query models, e.g., the (augmented) general model.
估算数据流中的子图数量是一个基本问题，在过去十年中受到了极大关注。在本文中，我们给出了改进的流算法，当输入图 G 表示为 m 条边的流时，可近似计算任意子图 H 的出现次数，记为 #H。为了获得我们的算法，我们提供了一种通用变换，它能将查询访问模型中的恒定回合子线性时间图算法转换为恒定传递子线性空间图流算法。利用这种转换，我们得到了以下结果。- 我们给出了 Õ(mρ(H) /ε2⋅#H) 空间中 (1 ± ε)-approximating #H 的 3-pass turnstile 流算法，其中 ρ(H) 是 H 的边覆盖率分数。[PODS 2016]，他们给出了一种只需插入的 3 次流式算法，即如果给算法额外的度数神谕访问权限，则可以在Õ(m3/2/ε2 ⋅ #T)空间中逼近 (1 ± ε)#T 的三角形个数。- 我们提供了一种在Õ(m/λr-2 ε2 ⋅ #Kr)空间中用于(1 ± ε)逼近 #Kr 的恒通流算法，该算法适用于任意 r ≥ 3 的具有退化性 λ 的图 G，其中 Kr 是 r 个顶点上的一个簇。这解决了 Bera 和 Seshadhri [PODS 2020] 的猜想。更一般地说，我们的还原将查询算法的适应性与相应流算法的通过复杂度联系起来，它适用于标准亚线性时间图查询模型中的所有算法，例如（增强的）一般模型。
{"title":"Approximately Counting Subgraphs in Data Streams","authors":"Hendrik Fichtenberger, Pan Peng","doi":"10.1145/3517804.3524145","DOIUrl":"https://doi.org/10.1145/3517804.3524145","url":null,"abstract":"Estimating the number of subgraphs in data streams is a fundamental problem that has received great attention in the past decade. In this paper, we give improved streaming algorithms for approximately counting the number of occurrences of an arbitrary subgraph H, denoted #H, when the input graph G is represented as a stream of m edges. To obtain our algorithms, we provide a generic transformation that converts constant-round sublinear-time graph algorithms in the query access model to constant-pass sublinear-space graph streaming algorithms. Using this transformation, we obtain the following results. • We give a 3-pass turnstile streaming algorithm for (1 ± ε)-approximating #H in Õ(mρ(H) /ε2⋅#H) space, where ρ(H) is the fractional edge-cover of H. This improves upon and generalizes a result of McGregor et al. [PODS 2016], who gave a 3-pass insertion-only streaming algorithm for (1 ± ε)-approximating the number #T of triangles in Õ(m3/2/ε2 ⋅ #T) space if the algorithm is given additional oracle access to the degrees.• We provide a constant-pass streaming algorithm for (1 ± ε)-approximating #Kr in Õ(m/λr-2 ε2 ⋅ #Kr) space for any r ≥ 3, in a graph G with degeneracy λ, where Kr is a clique on r vertices. This resolves a conjecture by Bera and Seshadhri [PODS 2020]. More generally, our reduction relates the adaptivity of a query algorithm to the pass complexity of a corresponding streaming algorithm, and it is applicable to all algorithms in standard sublinear-time graph query models, e.g., the (augmented) general model.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127348018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Since 2005, significant progress has been made in the problem of Consistent Query Answering (CQA) with respect to primary keys. In this problem, the input is a database instance that may violate one or more primary key constraints. A repair is defined as a maximal subinstance that satisfies all primary keys. Given a Boolean query q, the question then is whether q holds true in every repair. So far, theoretical research in this field has not addressed the combination of primary key and foreign key constraints, despite the importance of referential integrity in database systems. This paper addresses the problem of CQA with respect to both primary keys and foreign keys. In this setting, it is natural to adopt the notion of symmetric-difference repairs, because foreign keys can be repaired by inserting new tuples. We consider the case where foreign keys are unary, and queries are conjunctive queries without self-joins. In this setting, we characterize the boundary between those CQA problems that admit a consistent first-order rewriting, and those that do not.
{"title":"A Dichotomy in Consistent Query Answering for Primary Keys and Unary Foreign Keys","authors":"Miika Hannula, J. Wijsen","doi":"10.1145/3517804.3524157","DOIUrl":"https://doi.org/10.1145/3517804.3524157","url":null,"abstract":"Since 2005, significant progress has been made in the problem of Consistent Query Answering (CQA) with respect to primary keys. In this problem, the input is a database instance that may violate one or more primary key constraints. A repair is defined as a maximal subinstance that satisfies all primary keys. Given a Boolean query q, the question then is whether q holds true in every repair. So far, theoretical research in this field has not addressed the combination of primary key and foreign key constraints, despite the importance of referential integrity in database systems. This paper addresses the problem of CQA with respect to both primary keys and foreign keys. In this setting, it is natural to adopt the notion of symmetric-difference repairs, because foreign keys can be repaired by inserting new tuples. We consider the case where foreign keys are unary, and queries are conjunctive queries without self-joins. In this setting, we characterize the boundary between those CQA problems that admit a consistent first-order rewriting, and those that do not.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128356319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the enumeration of answers to ontology-mediated queries (OMQs) where the ontology is a set of guarded TGDs or formulated in the description logic ELI and the query is a conjunctive query (CQ). In addition to the traditional notion of an answer, we propose and study two novel notions of partial answers that can take into account nulls generated by existential quantifiers in the ontology. Our main result is that enumeration of the traditional complete answers and of both kinds of partial answers is possible with linear-time preprocessing and constant delay for OMQs that are both acyclic and free-connex acyclic. We also provide partially matching lower bounds. Similar results are obtained for the related problems of testing a single answer in linear time and of testing multiple answers in constant time after linear time preprocessing. In both cases, the border between tractability and intractability is characterized by similar, but slightly different acyclicity properties.
{"title":"Efficiently Enumerating Answers to Ontology-Mediated Queries","authors":"C. Lutz, Marcin Przybylko","doi":"10.1145/3517804.3524166","DOIUrl":"https://doi.org/10.1145/3517804.3524166","url":null,"abstract":"We study the enumeration of answers to ontology-mediated queries (OMQs) where the ontology is a set of guarded TGDs or formulated in the description logic ELI and the query is a conjunctive query (CQ). In addition to the traditional notion of an answer, we propose and study two novel notions of partial answers that can take into account nulls generated by existential quantifiers in the ontology. Our main result is that enumeration of the traditional complete answers and of both kinds of partial answers is possible with linear-time preprocessing and constant delay for OMQs that are both acyclic and free-connex acyclic. We also provide partially matching lower bounds. Similar results are obtained for the related problems of testing a single answer in linear time and of testing multiple answers in constant time after linear time preprocessing. In both cases, the border between tractability and intractability is characterized by similar, but slightly different acyclicity properties.","PeriodicalId":230606,"journal":{"name":"Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126467821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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