Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.19
Bas Ketsman, Christoph E. Koch
Positive Datalog has several nice properties that are lost when the language is extended with negation. One example is that fixpoints of positive Datalog programs are robust w.r.t. the order in which facts are inserted, which facilitates efficient evaluation of such programs in distributed environments. A natural question to ask, given a (stratified) Datalog program with negation, is whether an equivalent positive Datalog program exists. In this context, it is known that positive Datalog can express only a strict subset of the monotone queries, yet the exact relationship between the positive and monotone fragments of semi-positive and stratified Datalog was previously left open. In this paper, we complete the picture by showing that monotone queries expressible in semi-positive Datalog exist which are not expressible in positive Datalog. To provide additional insight into this gap, we also characterize a large class of semi-positive Datalog programs for which the dichotomy ‘monotone if and only if rewritable to positive Datalog’ holds. Finally, we give best-effort techniques to reduce the amount of negation that is exhibited by a program, even if the program is not monotone. 2012 ACM Subject Classification Information systems → Relational database query languages; Theory of computation → Constraint and logic programming
{"title":"Datalog with Negation and Monotonicity","authors":"Bas Ketsman, Christoph E. Koch","doi":"10.4230/LIPIcs.ICDT.2020.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.19","url":null,"abstract":"Positive Datalog has several nice properties that are lost when the language is extended with negation. One example is that fixpoints of positive Datalog programs are robust w.r.t. the order in which facts are inserted, which facilitates efficient evaluation of such programs in distributed environments. A natural question to ask, given a (stratified) Datalog program with negation, is whether an equivalent positive Datalog program exists. In this context, it is known that positive Datalog can express only a strict subset of the monotone queries, yet the exact relationship between the positive and monotone fragments of semi-positive and stratified Datalog was previously left open. In this paper, we complete the picture by showing that monotone queries expressible in semi-positive Datalog exist which are not expressible in positive Datalog. To provide additional insight into this gap, we also characterize a large class of semi-positive Datalog programs for which the dichotomy ‘monotone if and only if rewritable to positive Datalog’ holds. Finally, we give best-effort techniques to reduce the amount of negation that is exhibited by a program, even if the program is not monotone. 2012 ACM Subject Classification Information systems → Relational database query languages; Theory of computation → Constraint and logic programming","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81254388","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.7
Y. Chen, K. Yi
Computing joins is expensive, and often unnecessary when the output size is large. In 1999, Chaudhuri et al. [7] posed the problem of random sampling over joins as a potentially effective approach to avoiding computing the join in full, while obtaining important statistical information about the join results. Unfortunately, no significant progress has been made in the last 20 years, except for the case of acyclic joins. In this paper, we present the first non-trivial result on sampling over cyclic joins. We show that after a linear-time preprocessing step, a join result can be drawn uniformly at random in expected time O(IN/OUT), where IN is known as the AGM bound of the join and OUT is its output size. This result holds for all joins on binary relations, as well as certain joins on relations of higher arity. We further show how this algorithm immediately leads to a join size estimation algorithm with the same running time. 2012 ACM Subject Classification Theory of computation → Database theory
计算连接的成本很高，而且当输出大小很大时通常没有必要。1999年，Chaudhuri等人[7]提出了连接上的随机抽样问题，作为一种潜在的有效方法，可以避免完全计算连接，同时获得有关连接结果的重要统计信息。不幸的是，在过去的20年里，除了无环连接的情况外，没有取得重大进展。本文给出了循环连接上采样的第一个非平凡结果。我们表明，在线性时间预处理步骤之后，可以在预期时间0 (in /OUT)内均匀随机地绘制连接结果，其中in称为连接的AGM边界，OUT是其输出大小。这个结果适用于所有二元关系上的连接，以及某些更高密度关系上的连接。我们将进一步展示该算法如何立即生成具有相同运行时间的连接大小估计算法。2012 ACM学科分类:计算理论→数据库理论
{"title":"Random Sampling and Size Estimation Over Cyclic Joins","authors":"Y. Chen, K. Yi","doi":"10.4230/LIPIcs.ICDT.2020.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.7","url":null,"abstract":"Computing joins is expensive, and often unnecessary when the output size is large. In 1999, Chaudhuri et al. [7] posed the problem of random sampling over joins as a potentially effective approach to avoiding computing the join in full, while obtaining important statistical information about the join results. Unfortunately, no significant progress has been made in the last 20 years, except for the case of acyclic joins. In this paper, we present the first non-trivial result on sampling over cyclic joins. We show that after a linear-time preprocessing step, a join result can be drawn uniformly at random in expected time O(IN/OUT), where IN is known as the AGM bound of the join and OUT is its output size. This result holds for all joins on binary relations, as well as certain joins on relations of higher arity. We further show how this algorithm immediately leads to a join size estimation algorithm with the same running time. 2012 ACM Subject Classification Theory of computation → Database theory","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84122544","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.12
Floris Geerts
We investigate when two graphs, represented by their adjacency matrices, can be distinguished by means of sentences formed in MATLANG, a matrix query language which supports a number of elementary linear algebra operators. When undirected graphs are concerned, and hence the adjacency matrices are real and symmetric, precise characterisations are in place when two graphs (i.e., their adjacency matrices) can be distinguished. Turning to directed graphs, one has to deal with asymmetric adjacency matrices. This complicates matters. Indeed, it requires to understand the more general problem of when two arbitrary matrices can be distinguished in MATLANG. We provide characterisations of the distinguishing power of MATLANG on real and complex matrices, and on adjacency matrices of directed graphs in particular. The proof techniques are a combination of insights from the symmetric matrix case and results from linear algebra and linear control theory. 2012 ACM Subject Classification Theory of computation → Database query languages (principles); Mathematics of computing → Graph theory
{"title":"When Can Matrix Query Languages Discern Matrices?","authors":"Floris Geerts","doi":"10.4230/LIPIcs.ICDT.2020.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.12","url":null,"abstract":"We investigate when two graphs, represented by their adjacency matrices, can be distinguished by means of sentences formed in MATLANG, a matrix query language which supports a number of elementary linear algebra operators. When undirected graphs are concerned, and hence the adjacency matrices are real and symmetric, precise characterisations are in place when two graphs (i.e., their adjacency matrices) can be distinguished. Turning to directed graphs, one has to deal with asymmetric adjacency matrices. This complicates matters. Indeed, it requires to understand the more general problem of when two arbitrary matrices can be distinguished in MATLANG. We provide characterisations of the distinguishing power of MATLANG on real and complex matrices, and on adjacency matrices of directed graphs in particular. The proof techniques are a combination of insights from the symmetric matrix case and results from linear algebra and linear control theory. 2012 ACM Subject Classification Theory of computation → Database query languages (principles); Mathematics of computing → Graph theory","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80514911","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.14
Alejandro Grez, Cristian Riveros
Complex event processing (CEP) has gained a lot of attention for evaluating complex patterns over high-throughput data streams. Recently, new algorithms for the evaluation of CEP patterns have emerged with strong guarantees of efficiency, i.e. constant update-time per tuple and constant-delay enumeration. Unfortunately, these techniques are restricted for patterns with local filters, limiting the possibility of using joins for correlating the data of events that are far apart. In this paper, we embark on the search for efficient evaluation algorithms of CEP patterns with joins. We start by formalizing the so-called partition-by operator, a standard operator in data stream management systems to correlate contiguous events on streams. Although this operator is a restricted version of a join query, we show that partition-by (without iteration) is equally expressive as hierarchical queries, the biggest class of full conjunctive queries that can be evaluated with constant update-time and constant-delay enumeration over streams. To evaluate queries with partition-by we introduce an automata model, called chain complex event automata (chain-CEA), an extension of complex event automata that can compare data values by using equalities and disequalities. We show that this model admits determinization and is expressive enough to capture queries with partition-by. More importantly, we provide an algorithm with constant update time and constant delay enumeration for evaluating any query definable by chain-CEA, showing that all CEP queries with partition-by can be evaluated with these strong guarantees of efficiency. 2012 ACM Subject Classification Information systems → Data streams; Theory of computation → Database query processing and optimization (theory); Theory of computation → Formal languages and automata theory; Theory of computation → Automata extensions
{"title":"Towards Streaming Evaluation of Queries with Correlation in Complex Event Processing","authors":"Alejandro Grez, Cristian Riveros","doi":"10.4230/LIPIcs.ICDT.2020.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.14","url":null,"abstract":"Complex event processing (CEP) has gained a lot of attention for evaluating complex patterns over high-throughput data streams. Recently, new algorithms for the evaluation of CEP patterns have emerged with strong guarantees of efficiency, i.e. constant update-time per tuple and constant-delay enumeration. Unfortunately, these techniques are restricted for patterns with local filters, limiting the possibility of using joins for correlating the data of events that are far apart. In this paper, we embark on the search for efficient evaluation algorithms of CEP patterns with joins. We start by formalizing the so-called partition-by operator, a standard operator in data stream management systems to correlate contiguous events on streams. Although this operator is a restricted version of a join query, we show that partition-by (without iteration) is equally expressive as hierarchical queries, the biggest class of full conjunctive queries that can be evaluated with constant update-time and constant-delay enumeration over streams. To evaluate queries with partition-by we introduce an automata model, called chain complex event automata (chain-CEA), an extension of complex event automata that can compare data values by using equalities and disequalities. We show that this model admits determinization and is expressive enough to capture queries with partition-by. More importantly, we provide an algorithm with constant update time and constant delay enumeration for evaluating any query definable by chain-CEA, showing that all CEP queries with partition-by can be evaluated with these strong guarantees of efficiency. 2012 ACM Subject Classification Information systems → Data streams; Theory of computation → Database query processing and optimization (theory); Theory of computation → Formal languages and automata theory; Theory of computation → Automata extensions","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89969179","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.2
J. Marcinkowski
This paper was written as the companion paper of the ICDT 2020 invited tutorial. Query determinacy is a broad topic, with literally hundreds of papers published since late 1980s. This paper is not going to be a “survey” but rather a personal perspective of a person somehow involved in the recent developments in the area. First I explain how, in the last 30+ years, the question of determinacy was formalized. There are many parameters here: obviously one needs to choose the query language of the available views and the query language of the query itself. But – surprisingly – there is also some choice regarding what the word “to compute” actually means in this context. Then I concentrate on certain variants of the decision problem of determinacy (for each choice of parameters there is one such problem) and explain how I understand the mechanisms rendering such variants of determinacy decidable or undecidable. This is on a rather informal level. No really new theorems are presented, but I show some improvements of existing theorems and also simplified proofs of some of the earlier results. 2012 ACM Subject Classification Theory of computation → Database theory
{"title":"What Makes a Variant of Query Determinacy (Un)Decidable? (Invited Talk)","authors":"J. Marcinkowski","doi":"10.4230/LIPIcs.ICDT.2020.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.2","url":null,"abstract":"This paper was written as the companion paper of the ICDT 2020 invited tutorial. Query determinacy is a broad topic, with literally hundreds of papers published since late 1980s. This paper is not going to be a “survey” but rather a personal perspective of a person somehow involved in the recent developments in the area. First I explain how, in the last 30+ years, the question of determinacy was formalized. There are many parameters here: obviously one needs to choose the query language of the available views and the query language of the query itself. But – surprisingly – there is also some choice regarding what the word “to compute” actually means in this context. Then I concentrate on certain variants of the decision problem of determinacy (for each choice of parameters there is one such problem) and explain how I understand the mechanisms rendering such variants of determinacy decidable or undecidable. This is on a rather informal level. No really new theorems are presented, but I show some improvements of existing theorems and also simplified proofs of some of the earlier results. 2012 ACM Subject Classification Theory of computation → Database theory","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74675508","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.1
B. Kimelfeld
{"title":"Facets of Probabilistic Databases (Invited Talk)","authors":"B. Kimelfeld","doi":"10.4230/LIPIcs.ICDT.2020.1","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.1","url":null,"abstract":"","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77527497","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.23
Cristian Riveros, J. Salas
We present the theoretical foundations of a new approach in centrality measures for graph data. The main principle of our approach is very simple: the more relevant subgraphs around a vertex, the more central it is in the network. We formalize the notion of “relevant subgraphs” by choosing a family of subgraphs that, give a graph G and a vertex v in G, it assigns a subset of connected subgraphs of G that contains v. Any of such families defines a measure of centrality by counting the number of subgraphs assigned to the vertex, i.e., a vertex will be more important for the network if it belongs to more subgraphs in the family. We show many examples of this approach and, in particular, we propose the all-subgraphs centrality, a centrality measure that takes every subgraph into account. We study fundamental properties over families of subgraphs that guarantee desirable properties over the corresponding centrality measure. Interestingly, all-subgraphs centrality satisfies all these properties, showing its robustness as a notion for centrality. Finally, we study the computational complexity of counting certain families of subgraphs and show a polynomial time algorithm to compute the all-subgraphs centrality for graphs with bounded tree width. 2012 ACM Subject Classification Mathematics of computing→ Graph theory; Information systems → Graph-based database models
{"title":"A Family of Centrality Measures for Graph Data Based on Subgraphs","authors":"Cristian Riveros, J. Salas","doi":"10.4230/LIPIcs.ICDT.2020.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.23","url":null,"abstract":"We present the theoretical foundations of a new approach in centrality measures for graph data. The main principle of our approach is very simple: the more relevant subgraphs around a vertex, the more central it is in the network. We formalize the notion of “relevant subgraphs” by choosing a family of subgraphs that, give a graph G and a vertex v in G, it assigns a subset of connected subgraphs of G that contains v. Any of such families defines a measure of centrality by counting the number of subgraphs assigned to the vertex, i.e., a vertex will be more important for the network if it belongs to more subgraphs in the family. We show many examples of this approach and, in particular, we propose the all-subgraphs centrality, a centrality measure that takes every subgraph into account. We study fundamental properties over families of subgraphs that guarantee desirable properties over the corresponding centrality measure. Interestingly, all-subgraphs centrality satisfies all these properties, showing its robustness as a notion for centrality. Finally, we study the computational complexity of counting certain families of subgraphs and show a polynomial time algorithm to compute the all-subgraphs centrality for graphs with bounded tree width. 2012 ACM Subject Classification Mathematics of computing→ Graph theory; Information systems → Graph-based database models","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91536805","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.3
Juan L. Reutter
{"title":"Current Challenges in Graph Databases (Invited Talk)","authors":"Juan L. Reutter","doi":"10.4230/LIPIcs.ICDT.2020.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.3","url":null,"abstract":"","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74547742","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.9
Diego Figueira
We study the containment problem for UC2RPQ, that is, two-way Regular Path Queries, closed under conjunction, projection and union. We show a dichotomy property between PSpace-c and ExpSpace-c based on a property on the underlying graph of queries. We show that for any class C of graphs, the containment problem for queries whose underlying graph is in C is in PSpace if and only if C has bounded bridgewidth. Bridgewidth is a graph measure we introduce to this end, defined as the maximum size of a minimal edge separator of a graph. 2012 ACM Subject Classification Information systems → Graph-based database models; Information systems → Resource Description Framework (RDF); Mathematics of computing → Graph theory; Theory of computation → Formal languages and automata theory
{"title":"Containment of UC2RPQ: The Hard and Easy Cases","authors":"Diego Figueira","doi":"10.4230/LIPIcs.ICDT.2020.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.9","url":null,"abstract":"We study the containment problem for UC2RPQ, that is, two-way Regular Path Queries, closed under conjunction, projection and union. We show a dichotomy property between PSpace-c and ExpSpace-c based on a property on the underlying graph of queries. We show that for any class C of graphs, the containment problem for queries whose underlying graph is in C is in PSpace if and only if C has bounded bridgewidth. Bridgewidth is a graph measure we introduce to this end, defined as the maximum size of a minimal edge separator of a graph. 2012 ACM Subject Classification Information systems → Graph-based database models; Information systems → Resource Description Framework (RDF); Mathematics of computing → Graph theory; Theory of computation → Formal languages and automata theory","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89024977","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 : 2020-01-01DOI: 10.4230/LIPIcs.ICDT.2020.25
Yufei Tao
In PODS'17, Ketsman and Suciu gave an algorithm in the MPC model for computing the result of any natural join where every input relation has two attributes. Achieving an optimal load O(m/p^{1/ρ}) - where m is the total size of the input relations, p the number of machines, and ρ the fractional edge covering number of the join - their algorithm requires 7 rounds to finish. This paper presents a simpler algorithm that ensures the same load with 3 rounds (in fact, the second round incurs only a load of O(p²) to transmit certain statistics to assist machine allocation in the last round). Our algorithm is made possible by a new theorem that provides fresh insight on the structure of the problem, and brings us closer to understanding the intrinsic reason why joins on binary relations can be settled with load O(m/p^{1/ρ}).
{"title":"A Simple Parallel Algorithm for Natural Joins on Binary Relations","authors":"Yufei Tao","doi":"10.4230/LIPIcs.ICDT.2020.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICDT.2020.25","url":null,"abstract":"In PODS'17, Ketsman and Suciu gave an algorithm in the MPC model for computing the result of any natural join where every input relation has two attributes. Achieving an optimal load O(m/p^{1/ρ}) - where m is the total size of the input relations, p the number of machines, and ρ the fractional edge covering number of the join - their algorithm requires 7 rounds to finish. This paper presents a simpler algorithm that ensures the same load with 3 rounds (in fact, the second round incurs only a load of O(p²) to transmit certain statistics to assist machine allocation in the last round). Our algorithm is made possible by a new theorem that provides fresh insight on the structure of the problem, and brings us closer to understanding the intrinsic reason why joins on binary relations can be settled with load O(m/p^{1/ρ}).","PeriodicalId":90482,"journal":{"name":"Database theory-- ICDT : International Conference ... proceedings. International Conference on Database Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73057354","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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