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

2005
*
arXiv
*
pre-print

In this paper, we revisit the complexity

arXiv:cs/0507020v1
fatcat:mzjuoylhtrf2nf5upoioy3ono4
*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*. ...##
###
First-order queries on structures of bounded degree are computable with constant delay

2007
*
ACM Transactions on Computational Logic
*

In this paper, we revisit the complexity

doi:10.1145/1276920.1276923
fatcat:phru773k5jblxc2ohfgvg4ctn4
*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*. ...##
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Enumerating with constant delay the answers to a query

2013
*
Proceedings of the 16th International Conference on Database Theory - ICDT '13
*

We survey recent results about enumerating

doi:10.1145/2448496.2448498
dblp:conf/icdt/Segoufin13
fatcat:knkcl5pm2vebjfc5o6erez3yuu
*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. ...##
###
A glimpse on constant delay enumeration (Invited Talk)

2014
*
Symposium on Theoretical Aspects of Computer Science
*

We focus

doi:10.4230/lipics.stacs.2014.13
dblp:conf/stacs/Segoufin14
fatcat:yi6xqnceejdzxaof667rw6q2r4
*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. ...##
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First-order query evaluation on structures of bounded degree

2011
*
Logical Methods in Computer Science
*

We consider the enumeration problem

doi:10.2168/lmcs-7(2:20)2011
fatcat:4774a3niarcu3nxj2dfglzjqaq
*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. ...##
###
Dynamic Query Evaluation Over Structures with Low Degree
[article]

2020
*
arXiv
*
pre-print

Secondly, for classes

arXiv:2010.02982v1
fatcat:fooveztqznemzp34knverynfg4
*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*...##
###
Enumerating Answers to First-Order Queries over Databases of Low Degree
[article]

2022
*
arXiv
*
pre-print

to a

arXiv:2010.08382v4
fatcat:wd7wdkcihbgozclg3hu23pqj5i
*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. ...##
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First-order queries on classes of structures with bounded expansion
[article]

2020
*
arXiv
*
pre-print

Moreover, we show that answers to

arXiv:1802.04613v4
fatcat:cjim3qgvfbanre37pa4hyqwfeq
*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 )| # . ...##
###
First-order queries on classes of structures with bounded expansion

2018
*
Logical Methods in Computer Science
*

Moreover, we show that answers to

doi:10.23638/lmcs-16(1:25)2020
fatcat:lpbscjojtffgbclbhhiy633gua
*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 )| # . ...##
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Enumerating answers to first-order queries over databases of low degree

2014
*
Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '14
*

Typical examples

doi:10.1145/2594538.2594539
dblp:conf/pods/DurandSS14
fatcat:mzxeq7zrlvfezmz5ik5f5pn7fu
*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. ...##
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Enumeration of first-order queries on classes of structures with bounded expansion

2013
*
Proceedings of the 32nd symposium on Principles of database systems - PODS '13
*

We

doi:10.1145/2463664.2463667
dblp:conf/pods/KazanaS13
fatcat:6rrguc6x4fa4tmzkoiywbmb3la
*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] . ...##
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Constant Delay Enumeration for FO Queries over Databases with Local Bounded Expansion

2017
*
International Conference on Database Theory
*

We show that

doi:10.4230/lipics.icdt.2017.20
dblp:conf/icdt/SegoufinV17
fatcat:lyvhyunecng2lfnjdczvvy4xh4
*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. ...##
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Computing thejth solution of a first-order query

2008
*
RAIRO - Theoretical Informatics and Applications
*

We design algorithms

doi:10.1051/ita:2007046
fatcat:ab3ki2rkufa4hbk5l7bej7fmoy
*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. ...##
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Constant Delay Enumeration for Conjunctive Queries

2015
*
SIGMOD record
*

We focus

doi:10.1145/2783888.2783894
fatcat:vpya5xdg4vgzhfzockebesoqdy
*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. ...##
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Answering FO+MOD Queries under Updates on Bounded Degree Databases

2018
*
ACM Transactions on Database Systems
*

Kazana and Segoufin [12] also showed that counting the number

doi:10.1145/3232056
fatcat:43y7di3muvh3vg6vtzbvij4xdm
*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 ...
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