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Towards Tractable Algebras for Bags

1996
*
Journal of computer and system sciences (Print)
*

*Bags*, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of

*algebras*

*for*manipulating

*bags*. ... We show that the

*bag*

*algebra*is more expressive than the nested relation

*algebra*(at all levels of nesting), and that the di erence may be subtle. ... We studied an

*algebra*

*for*

*bags*, which extends the relational

*algebra*. Interestingly, we proved that without

*bag*nesting it constitutes a

*tractable*query language (LOGSPACE). ...

##
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Page 1261 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

Summary: “The goal of this paper is to study

*tractable*iteration mechanisms*for**bags*. ... We study two constructs*for*controlling*tractability*of iteration over*bags*. The 99b:68055 deflationary fixpoint construct keeps removing elements from a*bag*until a fixpoint is reached. ...##
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Page 7804 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
*
Mathematical Reviews
*

{

*For*the entire collection see MR 97k:68008. } 97m:68046 68P15 68Q15 Grumbach, Stéphane (F-INRIA; Le Chesnay); Milo, Tova (IL-TLAV-C; Tel Aviv)*Towards**tractable**algebras**for**bags*. ... The present authors make a similar study*for*a model based on multi-sets or*bags*, rather than ordinary sets. They define an analogous*bag**algebra*, and consider a similar hierarchy BALG*, k > 1. ...##
###
Fragments of bag relational algebra: Expressiveness and certain answers

2020
*
Information Systems
*

Thus, as D ′ ranges over D , we have a range of numbers that define an interval between min(ā, q, D) = min Complexity of min

doi:10.1016/j.is.2020.101604
fatcat:krwxwaozxvfjbdm7g3wpbzmm2y
*For*fragments in the shaded area, computing min(ā, q, D) is*tractable*, and it ... Under*bag*semantics, we have more information:*for*each tuple, we know the number # (ā , q(D ′ ) ) of occurrences ofā in q(D ′ ). ... Acknowledgments The authors would like to thank the anonymous reviewers*for*their constructive comments and suggestions, which have contributed to the improvement of this work. ...##
###
Tractability in constraint satisfaction problems: a survey

2015
*
Constraints
*

Acknowledgments We are grateful to Peter Jeavons and StanislavŽivný

doi:10.1007/s10601-015-9198-6
fatcat:fl7kxmceh5bqzpyd2c37rtohii
*for*their detailed comments on a first draft of this paper, and to the reviewers*for*their constructive comments. ...*for*each*bag*. ... (2)*for*every vertex v, the*bags*containing v form a connected subtree) except that instead of there being,*for*each*bag*, w hyperedges covering that*bag*, there is now a fractional edge cover ofweight w ...##
###
The HOMFLY-PT Polynomial is Fixed-Parameter Tractable

2018
*
International Symposium on Computational Geometry
*

Here we show that computing HOMFLY-PT is fixed-parameter

doi:10.4230/lipics.socg.2018.18
dblp:conf/compgeom/Burton18
fatcat:eokgxyto6bekbd5noge2hvnyba
*tractable*in the treewidth, and we give the first sub-exponential time algorithm to compute it*for*arbitrary links. ... It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter*tractable*in the treewidth of the link diagram, but the parameterised complexity of the more powerful HOMFLY-PT polynomial ... Then T has a unique forget*bag**for*which c is the forgotten vertex. Proof. Since the root*bag*of T is empty, there must be some forget*bag**for*which c is the forgotten vertex. ...##
###
The HOMFLY-PT polynomial is fixed-parameter tractable
[article]

2017
*
arXiv
*
pre-print

Here we show that computing HOMFLY-PT is fixed-parameter

arXiv:1712.05776v1
fatcat:rapfx45qebedzf7ffaqeijzq6i
*tractable*in the treewidth, and we give the first sub-exponential time algorithm to compute it*for*arbitrary links. ... It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter*tractable*in the treewidth of the link diagram, but the parameterised complexity of the more powerful HOMFLY-PT polynomial ... of Seifert circles [16, 17] , and the complexity of tangles in an*algebraic*presentation [16] . ...##
###
Page 1900 of Mathematical Reviews Vol. , Issue 97C
[page]

1997
*
Mathematical Reviews
*

Swami, Selectivity and cost estimation

*for*joins based on random sam- pling (550-569); Stéphane Grumbach and Tova Milo,*Towards**tractable**algebras**for**bags*(570-588); Paris Kanellakis, Sridhar Ramaswamy ... the relational*algebra*(537-549); Peter J. ...##
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Myths of Priority and Unity in Mathematics Learning

2018
*
Education Sciences
*

The myths we will discuss involve the order in which mathematical ideas are learnable and the "unity" of mathematical topics, with special attention to

doi:10.3390/educsci8020085
fatcat:g6ddjw4hgbherffdp5p64ftzje
*algebra*. ... But why keep these two elements of*algebra*together as one unitary*Algebra*? The first, the use of*algebraic*notation as language, is*tractable*in first and second grade (see, e.g., [16, 17, 20] ). ... But why keep these two elements of*algebra*together as one unitary*Algebra*? The first, the use of*algebraic*notation as language, is*tractable*in first and second grade (see, e.g., [16, 17, 20] ). ...##
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Editing the Simplest Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

As a special case, we give a tight time bound

doi:10.1007/978-3-319-04657-0_24
fatcat:sxcvuqi5dbgdppw2hxc7cbvlke
*for*edge deletion to obtain a single clique and isolated vertices, and we round up this study with NP-completeness results*for*a number of target graphs. ... The problem came up in practice, in mining a huge word similarity graph*for*well structured word clusters. It also adds to the rich field of graph modification problems. ... The authors would also like to thank Gabriele Capannini*for*sharing the data and discussing the applications, and Henning Fernau*for*intensive discussions of some open problems during a short visit at ...##
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Fixed-Parameter Tractable Canonization and Isomorphism Test for Graphs of Bounded Treewidth

2017
*
SIAM journal on computing (Print)
*

We give a fixed-parameter

doi:10.1137/140999980
fatcat:ve2dhxxejjfozlwjfta4zccb6e
*tractable*algorithm that, given a parameter k and two graphs G 1 , G 2 , either concludes that one of these graphs has treewidth at least k, or determines whether G 1 and G 2 ... way a graph c(G) that is isomorphic to G; • finds an isomorphism-invariant construction term -an*algebraic*expression that encodes G together with a tree decomposition of G of width less than k. ... Furthermore, we thank anonymous reviewers*for*extensive comments, in particular*for*pointing out that bootstraping Theorem 6.1 with the algorithm of Bodlaender [6] gives a better bound on the number ...##
###
Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
[chapter]

2020
*
Lecture Notes in Computer Science
*

Finally, we provide nested DP algorithms and implementations relying on database technology

doi:10.1007/978-3-030-51825-7_25
fatcat:5cdjcgdqrfgzrckiqrnzdox2qy
*for*variants and extensions of Boolean satisfiability. ... While numerous theoretical results establish*tractability*under the assumption of fixed treewidth, the practical success of exploiting this parameter is far behind what theoretical runtime bounds have ...*For*several problems hard*for*complexity class NP, there are results [12] showing socalled (fixed-parameter)*tractability*, which indicates a fixed-parameter*tractable*(FPT) algorithm running in polynomial ...##
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Recognition of complex events in open-source web-scale videos

2013
*
Proceedings of the 21st ACM international conference on Multimedia - MM '13
*

based representation of dominant camera motion present in video shots which can be used as a complementary feature

doi:10.1145/2502081.2502210
dblp:conf/mm/Bhattacharya13
fatcat:nazmpy3ftfau5nqv6d5bmhgjei
*for*video analysis. ... lowest level, our contributions include (a) compact covariance descriptors of appearance and motion features used in sparse coding framework to recognize realistic actions and gestures, and (b) a Lie-*algebra*... This encourages us to evaluate our method*for*complex event recognition in challenging datasets [3, 4] , which demonstrates conclusive evidence*towards*its applicability in opensource video analysis ...##
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Provenance for aggregate queries

2011
*
Proceedings of the 30th symposium on Principles of database systems of data - PODS '11
*

We realize this approach in a concrete construction, first

doi:10.1145/1989284.1989302
dblp:conf/pods/AmsterdamerDT11
fatcat:g7soooumoravfns24ykag7cgmq
*for*"simple" queries where the aggregation operator is the last one applied, and then*for*arbitrary (positive) relational*algebra*queries with ... We study in this paper provenance information*for*queries with aggregation. ... Val Tannen is grateful to Christoph Koch*for*discussions on the relationship between aggregates and difference and to Vittorio Perduca*for*discussions on the tensor product constructions. ...##
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Algorithms for algebraic path properties in concurrent systems of constant treewidth components

2016
*
SIGPLAN notices
*

We study algorithmic questions

doi:10.1145/2914770.2837624
fatcat:ueekz2sd7jepjpckibhg63xg24
*for*concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are*algebraic*with semiring operations. ... The*algebraic*path properties can model dataflow analysis problems, the shortest path problem, and many other natural properties that arise in program analysis. ... It suffices to show that*for*every*bag*B, we have |NhpBq| ď α´1 " 2¨p2{δq¨λ´1. Assume*towards*contradiction otherwise. Let B be the first*bag*that Rank assigned a rank such that |NhpBq| ě 2¨p2{δq¨λ. ...
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