Pub Date : 2022-01-01DOI: 10.4230/LIPIcs.ICDT.2022.18
Sarah Kleest-Meißner, Rebecca Sattler, Markus L. Schmid, Nicole Schweikardt, M. Weidlich
We introduce subsequence-queries with wildcards and gap-size constraints (swg-queries, for short) as a tool for querying event traces. An swg-query q is given by a string s over an alphabet of variables and types, a global window size w , and a tuple c = (( c − 1 , c +1 ) , ( c − 2 , c +2 ) , . . . , ( c −| s |− 1 , c + | s |− 1 )) of local gap-size constraints over N × ( N ∪ {∞} ). The query q matches in a trace t (i. e., a sequence of types) if the variables can uniformly be substituted by types such that the resulting string occurs in t as a subsequence that spans an area of length at most w , and the i th gap of the subsequence (i. e., the distance between the i th and ( i +1) th position of the subsequence) has length at least c − i and at most c + i . We formalise and investigate the task of discovering an swg-query that describes best the traces from a given sample S of traces, and we present an algorithm solving this task. As a central component, our algorithm repeatedly solves the matching problem (i. e., deciding whether a given query q matches in a given trace t ), which is an NP-complete problem (in combined complexity). Hence, the matching problem is of special interest in the context of query discovery, and we therefore subject it to a detailed (parameterised) complexity analysis to identify tractable subclasses, which lead to tractable subclasses of the discovery problem as well. We complement this by a reduction proving Proof sketch. A natural brute-force approach is as follows: Upon input of an swg-query q = ( s, w, c ) and a trace t , we enumerate all mappings π : repvars ( q ) → types ( t ), and for each such mapping, we construct a regular expression R π that describes all traces t ′ for which there exists a substitution µ : vars ( q ) ∪ Γ → Γ such that µ is an extension of π and µ ( s ) ≼ e t ′ for some embedding e that satisfies w and c . Then, we only have to check for each of these mappings π , if the regular expression R π matches in t . Another approach is to enumerate all embeddings e : [ | s | ] → [ | t | ] that satisfy w and c and check for each such embedding e whether µ ( s ) ≼ e t for some substitution µ (which can be done in time O( | s | ), since µ must satisfy µ ( s ) = t [ e (1)] t [ e (2)] . . . t [ e ( | s | )]). From these two algorithms and the obvious dependencies between the parameters, we can directly conclude the statements of the theorem.
我们引入带有通配符和间隙大小约束的子查询(简称swg查询)作为查询事件跟踪的工具。swg查询q由变量和类型字母表上的字符串s、全局窗口大小w和元组c = ((c−1,c +1)， (c−2,c +2)，…， (c−| s |−1,c + | s |−1))在N × (N∪{∞})上的局部间隙大小约束。查询问匹配跟踪t(即一系列类型)如果一致可以替换的变量类型,这样生成的字符串出现在t作为子序列跨度的长度最多w,我th差距的子序列(即我th和之间的距离(i + 1) th子序列的位置)长度至少c−我最多和c +。我们形式化并研究了从给定的轨迹样本S中发现最能描述轨迹的swg查询的任务，并提出了解决该任务的算法。作为中心组件，我们的算法反复解决匹配问题(即决定给定查询q在给定跟踪t中是否匹配)，这是一个np完全问题(组合复杂度)。因此，匹配问题在查询发现的上下文中特别重要，因此我们对其进行了详细的(参数化的)复杂性分析，以识别可处理的子类，这也会导致发现问题的可处理子类。我们补充了一个简化证明的证明草图。自然蛮力方法如下:在输入一个swg-query q = (s, w c)和跟踪t,我们列举所有映射π:repvars (q)→类型(t),对于每一次这样的映射,我们构造一个正则表达式Rπ,描述了所有的痕迹t’的存在一个替换µ:var (q)∪Γ→Γ这样µ是π的扩展和µ(s)≼e t '对于一些嵌入满足w e和c。然后，我们只需要检查每一个映射，如果正则表达式R在t中匹配。另一种方法是枚举满足w和c的所有嵌入e: [| s |]→[| t |]，并检查每个这样的嵌入e是否对某些替换μ(这可以在时间O(| s |)中完成)，因为µ必须满足µ(s) = t [e (1)] t [e(2)]。T [e (| s |)])。从这两种算法和参数之间明显的依赖关系，我们可以直接得出定理的表述。
{"title":"Discovering Event Queries from Traces: Laying Foundations for Subsequence-Queries with Wildcards and Gap-Size Constraints","authors":"Sarah Kleest-Meißner, Rebecca Sattler, Markus L. Schmid, Nicole Schweikardt, M. Weidlich","doi":"10.4230/LIPIcs.ICDT.2022.18","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.18","url":null,"abstract":"We introduce subsequence-queries with wildcards and gap-size constraints (swg-queries, for short) as a tool for querying event traces. An swg-query q is given by a string s over an alphabet of variables and types, a global window size w , and a tuple c = (( c − 1 , c +1 ) , ( c − 2 , c +2 ) , . . . , ( c −| s |− 1 , c + | s |− 1 )) of local gap-size constraints over N × ( N ∪ {∞} ). The query q matches in a trace t (i. e., a sequence of types) if the variables can uniformly be substituted by types such that the resulting string occurs in t as a subsequence that spans an area of length at most w , and the i th gap of the subsequence (i. e., the distance between the i th and ( i +1) th position of the subsequence) has length at least c − i and at most c + i . We formalise and investigate the task of discovering an swg-query that describes best the traces from a given sample S of traces, and we present an algorithm solving this task. As a central component, our algorithm repeatedly solves the matching problem (i. e., deciding whether a given query q matches in a given trace t ), which is an NP-complete problem (in combined complexity). Hence, the matching problem is of special interest in the context of query discovery, and we therefore subject it to a detailed (parameterised) complexity analysis to identify tractable subclasses, which lead to tractable subclasses of the discovery problem as well. We complement this by a reduction proving Proof sketch. A natural brute-force approach is as follows: Upon input of an swg-query q = ( s, w, c ) and a trace t , we enumerate all mappings π : repvars ( q ) → types ( t ), and for each such mapping, we construct a regular expression R π that describes all traces t ′ for which there exists a substitution µ : vars ( q ) ∪ Γ → Γ such that µ is an extension of π and µ ( s ) ≼ e t ′ for some embedding e that satisfies w and c . Then, we only have to check for each of these mappings π , if the regular expression R π matches in t . Another approach is to enumerate all embeddings e : [ | s | ] → [ | t | ] that satisfy w and c and check for each such embedding e whether µ ( s ) ≼ e t for some substitution µ (which can be done in time O( | s | ), since µ must satisfy µ ( s ) = t [ e (1)] t [ e (2)] . . . t [ e ( | s | )]). From these two algorithms and the obvious dependencies between the parameters, we can directly conclude the statements of the theorem.","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"27 1","pages":"18:1-18:21"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84278741","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}
Pub Date : 2022-01-01DOI: 10.4230/LIPIcs.ICDT.2022.15
B. Bogaerts, Maxim Jakubowski, J. V. D. Bussche
SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use four fundamental features that are not so common in description logics. These features are zero-or-one path expressions; equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inclusion constraints. The goal of this paper is to obtain a clear picture of the impact and expressiveness of these features and restrictions. We show that each of the four features is primitive: using the feature, one can express boolean queries that are not expressible without using the feature. We also show that the restriction that SHACL imposes on allowed targets is inessential, as long as closure constraints are not used.
{"title":"Expressiveness of SHACL Features","authors":"B. Bogaerts, Maxim Jakubowski, J. V. D. Bussche","doi":"10.4230/LIPIcs.ICDT.2022.15","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.15","url":null,"abstract":"SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use four fundamental features that are not so common in description logics. These features are zero-or-one path expressions; equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inclusion constraints. The goal of this paper is to obtain a clear picture of the impact and expressiveness of these features and restrictions. We show that each of the four features is primitive: using the feature, one can express boolean queries that are not expressible without using the feature. We also show that the restriction that SHACL imposes on allowed targets is inessential, as long as closure constraints are not used.","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"82 1","pages":"15:1-15:16"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79779248","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}
Pub Date : 2022-01-01DOI: 10.4230/LIPIcs.ICDT.2022.11
Martin Raszyk, D. Basin, S. Krstic, Dmitriy Traytel
The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management systems. We devise a new translation of an arbitrary RC query into two safe-range queries, for which the finiteness of the query’s evaluation result is guaranteed. Assuming an infinite domain, the two queries have the following meaning: The first is closed and characterizes the original query’s relative safety, i.e., whether given a fixed database, the original query evaluates to a finite relation. The second safe-range query is equivalent to the original query, if the latter is relatively safe. We compose our translation with other, more standard ones to ultimately obtain two SQL queries. This allows us to use standard database management systems to evaluate arbitrary RC queries. We show that our translation improves the time complexity over existing approaches, which we also empirically confirm in both realistic and synthetic experiments.
{"title":"Practical Relational Calculus Query Evaluation","authors":"Martin Raszyk, D. Basin, S. Krstic, Dmitriy Traytel","doi":"10.4230/LIPIcs.ICDT.2022.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.11","url":null,"abstract":"The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management systems. We devise a new translation of an arbitrary RC query into two safe-range queries, for which the finiteness of the query’s evaluation result is guaranteed. Assuming an infinite domain, the two queries have the following meaning: The first is closed and characterizes the original query’s relative safety, i.e., whether given a fixed database, the original query evaluates to a finite relation. The second safe-range query is equivalent to the original query, if the latter is relatively safe. We compose our translation with other, more standard ones to ultimately obtain two SQL queries. This allows us to use standard database management systems to evaluate arbitrary RC queries. We show that our translation improves the time complexity over existing approaches, which we also empirically confirm in both realistic and synthetic experiments.","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"1 1","pages":"11:1-11:21"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82452571","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}
Pub Date : 2022-01-01DOI: 10.4230/LIPIcs.ICDT.2022.1
H. Q. Ngo
{"title":"On an Information Theoretic Approach to Cardinality Estimation (Invited Talk)","authors":"H. Q. Ngo","doi":"10.4230/LIPIcs.ICDT.2022.1","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.1","url":null,"abstract":"","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"63 1","pages":"1:1-1:21"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83940460","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}
Pub Date : 2022-01-01DOI: 10.4230/LIPIcs.ICDT.2022.2
M. Arenas
{"title":"Counting the Solutions to a Query (Invited Talk)","authors":"M. Arenas","doi":"10.4230/LIPIcs.ICDT.2022.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.2","url":null,"abstract":"","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"11 1","pages":"2:1-2:1"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89252077","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}
Pub Date : 2022-01-01DOI: 10.4230/LIPIcs.ICDT.2022.3
Nofar Carmeli
The holy grail we strive for is, given a query, to identify an algorithm that answers it over general databases with optimal time guarantees for the specific query. In this tutorial, we focus on what can be seen as ideal time guarantees: linear preprocessing (needed to read the input) and constant time per answer (needed to print the output). We seek to understand which queries can be solved with these (or almost these) time guarantees and how. We start with the basic building blocks of database queries: joins, and slowly increase the expressivity by introducing projections and unions until we cover positive relational algebra. We first consider the task of enumerating all query answers and then discuss related, more demanding, tasks such as ordered enumeration and direct access to query answers. We investigate the challenges in answering such queries and provide algorithms and conditional lower bounds 2012 ACM Classification Theory of computation → Database query processing and
{"title":"Answering Unions of Conjunctive Queries with Ideal Time Guarantees (Invited Talk)","authors":"Nofar Carmeli","doi":"10.4230/LIPIcs.ICDT.2022.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.3","url":null,"abstract":"The holy grail we strive for is, given a query, to identify an algorithm that answers it over general databases with optimal time guarantees for the specific query. In this tutorial, we focus on what can be seen as ideal time guarantees: linear preprocessing (needed to read the input) and constant time per answer (needed to print the output). We seek to understand which queries can be solved with these (or almost these) time guarantees and how. We start with the basic building blocks of database queries: joins, and slowly increase the expressivity by introducing projections and unions until we cover positive relational algebra. We first consider the task of enumerating all query answers and then discuss related, more demanding, tasks such as ordered enumeration and direct access to query answers. We investigate the challenges in answering such queries and provide algorithms and conditional lower bounds 2012 ACM Classification Theory of computation → Database query processing and","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"13 1","pages":"3:1-3:1"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81977587","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}
Pub Date : 2021-12-27DOI: 10.4230/LIPIcs.ICDT.2023.12
Cristian Riveros, J. Salas, Oskar Skibski
Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused on classes of centrality measures. In this work, we provide a different approach by focusing on classes of graphs instead of classes of measures to understand the underlying principles among various measures. More precisely, we study the class of trees. We observe that even in fix{the} case of trees, there is no consensus on which node should be selected as the most central. To analyze the behavior of centrality measures on trees, we introduce a property of emph{tree rooting} that states a measure selects one or two adjacent nodes as the most important, and the importance decreases from them in all directions. This property is satisfied by closeness centrality but violated by PageRank. We show that, for several centrality measures that root trees, the comparison of adjacent nodes can be inferred by emph{potential functions} that assess the quality of trees. We use these functions to give fundamental insights on rooting and derive a characterization explaining why some measure root trees. Moreover, we provide an almost liner-time algorithm to compute the root of a graph by using potential functions. Finally, using a family of potential functions, we show that many ways of tree rooting exist with desirable properties.
{"title":"How Do Centrality Measures Choose the Root of Trees?","authors":"Cristian Riveros, J. Salas, Oskar Skibski","doi":"10.4230/LIPIcs.ICDT.2023.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2023.12","url":null,"abstract":"Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused on classes of centrality measures. In this work, we provide a different approach by focusing on classes of graphs instead of classes of measures to understand the underlying principles among various measures. More precisely, we study the class of trees. We observe that even in fix{the} case of trees, there is no consensus on which node should be selected as the most central. To analyze the behavior of centrality measures on trees, we introduce a property of emph{tree rooting} that states a measure selects one or two adjacent nodes as the most important, and the importance decreases from them in all directions. This property is satisfied by closeness centrality but violated by PageRank. We show that, for several centrality measures that root trees, the comparison of adjacent nodes can be inferred by emph{potential functions} that assess the quality of trees. We use these functions to give fundamental insights on rooting and derive a characterization explaining why some measure root trees. Moreover, we provide an almost liner-time algorithm to compute the root of a graph by using potential functions. Finally, using a family of potential functions, we show that many ways of tree rooting exist with desirable properties.","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"15 1","pages":"12:1-12:17"},"PeriodicalIF":0.0,"publicationDate":"2021-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88554988","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}
Pub Date : 2021-09-13DOI: 10.4230/LIPIcs.ICDT.2022.17
Jingfan Meng, Huayi Wang, Jun Xu, M. Ogihara
Efficient range-summability (ERS) of a long list of random variables is a fundamental algorithmic problem that has applications to three important database applications, namely, data stream processing, space-efficient histogram maintenance (SEHM), and approximate nearest neighbor searches (ANNS). In this work, we propose a novel dyadic simulation framework and develop three novel ERS solutions, namely Gaussian-dyadic simulation tree (DST), Cauchy-DST and Random Walk-DST, using it. We also propose novel rejection sampling techniques to make these solutions computationally efficient. Furthermore, we develop a novel k-wise independence theory that allows our ERS solutions to have both high computational efficiencies and strong provable independence guarantees.
{"title":"A Dyadic Simulation Approach to Efficient Range-Summability","authors":"Jingfan Meng, Huayi Wang, Jun Xu, M. Ogihara","doi":"10.4230/LIPIcs.ICDT.2022.17","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2022.17","url":null,"abstract":"Efficient range-summability (ERS) of a long list of random variables is a fundamental algorithmic problem that has applications to three important database applications, namely, data stream processing, space-efficient histogram maintenance (SEHM), and approximate nearest neighbor searches (ANNS). In this work, we propose a novel dyadic simulation framework and develop three novel ERS solutions, namely Gaussian-dyadic simulation tree (DST), Cauchy-DST and Random Walk-DST, using it. We also propose novel rejection sampling techniques to make these solutions computationally efficient. Furthermore, we develop a novel k-wise independence theory that allows our ERS solutions to have both high computational efficiencies and strong provable independence guarantees.","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"41 1","pages":"17:1-17:18"},"PeriodicalIF":0.0,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86879890","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}
Pub Date : 2021-01-11DOI: 10.4230/LIPIcs.ICDT.2021.14
Shaleen Deep, Xiao Hu, Paraschos Koutris
We investigate the enumeration of query results for an important subset of CQs with projections, namely star and path queries. The task is to design data structures and algorithms that allow for efficient enumeration with delay guarantees after a preprocessing phase. Our main contribution is a series of results based on the idea of interleaving precomputed output with further join processing to maintain delay guarantees, which maybe of independent interest. In particular, for star queries, we design combinatorial algorithms that provide instance-specific delay guarantees in linear preprocessing time. These algorithms improve upon the currently best known results. Further, we show how existing results can be improved upon by using fast matrix multiplication. We also present new results involving tradeoff between preprocessing time and delay guarantees for enumeration of path queries that contain projections. Boolean matrix multiplication is an important query that can be expressed as a CQ with projection where the join attribute is projected away. Our results can therefore also be interpreted as sparse, output-sensitive matrix multiplication with delay guarantees.
{"title":"Enumeration Algorithms for Conjunctive Queries with Projection","authors":"Shaleen Deep, Xiao Hu, Paraschos Koutris","doi":"10.4230/LIPIcs.ICDT.2021.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2021.14","url":null,"abstract":"We investigate the enumeration of query results for an important subset of CQs with projections, namely star and path queries. The task is to design data structures and algorithms that allow for efficient enumeration with delay guarantees after a preprocessing phase. Our main contribution is a series of results based on the idea of interleaving precomputed output with further join processing to maintain delay guarantees, which maybe of independent interest. In particular, for star queries, we design combinatorial algorithms that provide instance-specific delay guarantees in linear preprocessing time. These algorithms improve upon the currently best known results. Further, we show how existing results can be improved upon by using fast matrix multiplication. We also present new results involving tradeoff between preprocessing time and delay guarantees for enumeration of path queries that contain projections. Boolean matrix multiplication is an important query that can be expressed as a CQ with projection where the join attribute is projected away. Our results can therefore also be interpreted as sparse, output-sensitive matrix multiplication with delay guarantees.","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":"101 1","pages":"14:1-14:17"},"PeriodicalIF":0.0,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80744953","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}
Pub Date : 2021-01-06DOI: 10.4230/LIPIcs.ICDT.2021.19
Katrin Casel, Markus L. Schmid
A regular path query (RPQ) is a regular expression q that returns all node pairs (u, v) from a graph database that are connected by an arbitrary path labelled with a word from L(q). The obvious algorithmic approach to RPQ-evaluation (called PG-approach), i.e., constructing the product graph between an NFA for q and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs.
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