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First-order queries on structures of bounded degree are computable with constant delay [article]

Arnaud Durand, Etienne Grandjean
2005 arXiv   pre-print
In this paper, we revisit the complexity of the evaluation problem of not necessarily Boolean first-order queries over structures of bounded degree.  ...  then, it outputs all tuples one by one with a constant (i.e. depending on the size of the formula only) delay between each.  ...  We thank Ron Fagin for a very fruitful email exchange that lead us to define complexity notions about constant delay computation.  ... 
arXiv:cs/0507020v1 fatcat:mzjuoylhtrf2nf5upoioy3ono4

First-order queries on structures of bounded degree are computable with constant delay

Arnaud Durand, Etienne Grandjean
2007 ACM Transactions on Computational Logic  
In this paper, we revisit the complexity of the evaluation problem of not necessarily Boolean first-order (FO) queries over d-degree-bounded structures.  ...  step of time linear in the size of the structure and then, it outputs all solutions (i.e. tuples that satisfy the formula) one by one with a constant delay (i.e. depending on the size of the formula only  ...  We thank Ron Fagin for a very fruitful email exchange that lead us to define complexity notions about constant delay computations.  ... 
doi:10.1145/1276920.1276923 fatcat:phru773k5jblxc2ohfgvg4ctn4

Enumerating with constant delay the answers to a query

Luc Segoufin
2013 Proceedings of the 16th International Conference on Database Theory - ICDT '13  
We survey recent results about enumerating with constant delay the answers to a query over a database.  ...  one by one with constant time between any consecutive outputs.  ...  Acknowledgment: We are grateful to Cristina Sirangelo, Arnaud Durand, Wojtek Kazana and Yann Strozecki for their valuable comments on earlier version of this paper.  ... 
doi:10.1145/2448496.2448498 dblp:conf/icdt/Segoufin13 fatcat:knkcl5pm2vebjfc5o6erez3yuu

A glimpse on constant delay enumeration (Invited Talk)

Luc Segoufin, Marc Herbstritt
2014 Symposium on Theoretical Aspects of Computer Science  
We focus on the case where the enumeration is performed with a constant delay between any two consecutive solutions, after a linear time preprocessing. This cannot be always achieved.  ...  We survey some of the recent results about enumerating the answers to queries over a database.  ...  In order to enumerate this query with constant delay it is necessary to perform a preprocessing. We first decide on an arbitrary linear order on the domain of D.  ... 
doi:10.4230/lipics.stacs.2014.13 dblp:conf/stacs/Segoufin14 fatcat:yi6xqnceejdzxaof667rw6q2r4

First-order query evaluation on structures of bounded degree

Wojciech Kazana, Luc Segoufin, Leonid Libkin
2011 Logical Methods in Computer Science  
We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class.  ...  with no repetition and a constant delay between two consecutive outputs.  ...  Acknowledgement The authors wish to thank Dietrich Kuske and the anonymous referees for their constructive comments on earlier versions of this paper.  ... 
doi:10.2168/lmcs-7(2:20)2011 fatcat:4774a3niarcu3nxj2dfglzjqaq

Dynamic Query Evaluation Over Structures with Low Degree [article]

Alexandre Vigny
2020 arXiv   pre-print
Secondly, for classes of databases with bounded degree we show that, without increasing the preprocessing time, we can compute a data structure that does not depend on the query but only on its quantifier  ...  We consider the evaluation of first-order queries over classes of databases that have bounded degree and low degree.  ...  We obtain that: #α(G) = C We proved that over structures with bounded or low degree and for every first-order query, we can efficiently compute and recompute a data structure allowing to answer in constant  ... 
arXiv:2010.02982v1 fatcat:fooveztqznemzp34knverynfg4

Enumerating Answers to First-Order Queries over Databases of Low Degree [article]

Arnaud Durand, Nicole Schweikardt, Luc Segoufin
2022 arXiv   pre-print
to a query or enumerate the answers to a query with constant delay.  ...  Typical examples are databases of bounded degree or of degree bounded by log n.  ...  In order to enumerate q with constant delay over a class of low degree we proceed as follows.  ... 
arXiv:2010.08382v4 fatcat:wd7wdkcihbgozclg3hu23pqj5i

First-order queries on classes of structures with bounded expansion [article]

Wojtek Kazana, Luc Segoufin
2020 arXiv   pre-print
Moreover, we show that answers to first-order queries can be enumerated with constant delay after a linear time preprocessing.  ...  We consider the evaluation of first-order queries over classes of databases with bounded expansion.  ...  We can now use the inductive hypothesis on the size of ∆ = to both ψ − and ψ + in order to compute both |ψ − (f G )| # and |ψ + (f G )| # and derive |ψ(f G )| # .  ... 
arXiv:1802.04613v4 fatcat:cjim3qgvfbanre37pa4hyqwfeq

First-order queries on classes of structures with bounded expansion

Wojtek Kazana, Luc Segoufin
2018 Logical Methods in Computer Science  
Moreover, we show that answers to first-order queries can be enumerated with constant delay after a linear time preprocessing.  ...  We consider the evaluation of first-order queries over classes of databases with bounded expansion.  ...  We can now use the inductive hypothesis on the size of ∆ = to both ψ − and ψ + in order to compute both |ψ − (f G )| # and |ψ + (f G )| # and derive |ψ(f G )| # .  ... 
doi:10.23638/lmcs-16(1:25)2020 fatcat:lpbscjojtffgbclbhhiy633gua

Enumerating answers to first-order queries over databases of low degree

Arnaud Durand, Nicole Schweikardt, Luc Segoufin
2014 Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '14  
Typical examples are databases of bounded degree or of degree bounded by log n.  ...  It is known that over a class of databases having low degree, first-order boolean queries can be checked in pseudo-linear time, i.e. in time bounded by n 1+ε , for all ε.  ...  Consider again the query q of Example 1. In order to enumerate q with constant delay over a class of low degree we proceed as follows.  ... 
doi:10.1145/2594538.2594539 dblp:conf/pods/DurandSS14 fatcat:mzxeq7zrlvfezmz5ik5f5pn7fu

Enumeration of first-order queries on classes of structures with bounded expansion

Wojciech Kazana, Luc Segoufin
2013 Proceedings of the 32nd symposium on Principles of database systems - PODS '13  
We first give a different proof of this result. Moreover, we show that answers to first-order queries can be enumerated with constant delay after a linear time preprocessing.  ...  We consider the evaluation of first-order queries over classes of databases with bounded expansion.  ...  For the class of structures with bounded degree and FO queries the model checking is in FPL [20] and there also are constant delay enumeration algorithms [9, 13] .  ... 
doi:10.1145/2463664.2463667 dblp:conf/pods/KazanaS13 fatcat:6rrguc6x4fa4tmzkoiywbmb3la

Constant Delay Enumeration for FO Queries over Databases with Local Bounded Expansion

Luc Segoufin, Alexandre Vigny, Marc Herbstritt
2017 International Conference on Database Theory  
We show that first-order queries can be enumerated with constant delay after a pseudo-linear preprocessing over any class of databases having locally bounded expansion.  ...  We consider the evaluation of first-order queries over classes of databases with local bounded expansion.  ...  The enumeration of first-order query over class of graphs with local bounded expansion can be done with constant delay, after pseudo-linear preprocessing.  ... 
doi:10.4230/lipics.icdt.2017.20 dblp:conf/icdt/SegoufinV17 fatcat:lyvhyunecng2lfnjdczvvy4xh4

Computing thejth solution of a first-order query

Guillaume Bagan, Arnaud Durand, Etienne Grandjean, Frédéric Olive
2008 RAIRO - Theoretical Informatics and Applications  
We design algorithms of "optimal" data complexity for several natural problems about first-order queries on structures of bounded degree.  ...  Algorithms of "minimal" data complexity are presented for the following problems: given any first-order formula ϕ(v) and any structure S of bounded degree: (1) compute a random element of ϕ(S) = {a : (  ...  First-order logic over such structures is the analog of first-order logic over structures of bounded degree when dealing with functions instead of relations.  ... 
doi:10.1051/ita:2007046 fatcat:ab3ki2rkufa4hbk5l7bej7fmoy

Constant Delay Enumeration for Conjunctive Queries

Luc Segoufin
2015 SIGMOD record  
We focus on the case where the enumeration is performed with a constant delay between any two consecutive solutions, after a linear time preprocessing. This cannot be always achieved.  ...  It requires restricting either the class of queries or the class of databases. We consider conjunctive queries and describe several scenarios when this is possible.  ...  In order to enumerate this query with constant delay it is necessary to perform a preprocessing computing an index structure that can be used for enumeration. This is done as follows.  ... 
doi:10.1145/2783888.2783894 fatcat:vpya5xdg4vgzhfzockebesoqdy

Answering FO+MOD Queries under Updates on Bounded Degree Databases

Christoph Berkholz, Jens Keppeler, Nicole Schweikardt
2018 ACM Transactions on Database Systems  
Kazana and Segoufin [12] also showed that counting the number of result tuples of a k-ary first-order query on databases of bounded expansion (and hence also on databases of bounded degree) can be done  ...  Furthermore, after every update we are able to immediately enumerate the new query result with constant delay between the output tuples.  ...  More specifically: Are there efficient dynamic algorithms for evaluating (i.e., answering, testing, counting, or enumerating) results of first-order queries on other sparse classes of databases (e.g. planar  ... 
doi:10.1145/3232056 fatcat:43y7di3muvh3vg6vtzbvij4xdm
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