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Towards Tractable Algebras for Bags

Stéphane Grumbach, Tova Milo
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).  ... 
doi:10.1006/jcss.1996.0042 fatcat:6csdhuso4fdn3p75i56hecamry

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.  ... 

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

Marco Console, Paolo Guagliardo, Leonid Libkin
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 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.  ... 
doi:10.1016/j.is.2020.101604 fatcat:krwxwaozxvfjbdm7g3wpbzmm2y

Tractability in constraint satisfaction problems: a survey

Clément Carbonnel, Martin C. Cooper
2015 Constraints  
Acknowledgments We are grateful to Peter Jeavons and StanislavŽivný 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  ... 
doi:10.1007/s10601-015-9198-6 fatcat:fl7kxmceh5bqzpyd2c37rtohii

The HOMFLY-PT Polynomial is Fixed-Parameter Tractable

Benjamin A. Burton, Marc Herbstritt
2018 International Symposium on Computational Geometry  
Here we show that computing HOMFLY-PT is fixed-parameter 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.  ... 
doi:10.4230/lipics.socg.2018.18 dblp:conf/compgeom/Burton18 fatcat:eokgxyto6bekbd5noge2hvnyba

The HOMFLY-PT polynomial is fixed-parameter tractable [article]

Benjamin A. Burton
2017 arXiv   pre-print
Here we show that computing HOMFLY-PT is fixed-parameter 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] .  ... 
arXiv:1712.05776v1 fatcat:rapfx45qebedzf7ffaqeijzq6i

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.  ... 

Myths of Priority and Unity in Mathematics Learning

E. Goldenberg, Cynthia Carter
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 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] ).  ... 
doi:10.3390/educsci8020085 fatcat:g6ddjw4hgbherffdp5p64ftzje

Editing the Simplest Graphs [chapter]

Peter Damaschke, Olof Mogren
2014 Lecture Notes in Computer Science  
As a special case, we give a tight time bound 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  ... 
doi:10.1007/978-3-319-04657-0_24 fatcat:sxcvuqi5dbgdppw2hxc7cbvlke

Fixed-Parameter Tractable Canonization and Isomorphism Test for Graphs of Bounded Treewidth

Daniel Lokshtanov, Marcin Pilipczuk, Michał Pilipczuk, Saket Saurabh
2017 SIAM journal on computing (Print)  
We give a fixed-parameter 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  ... 
doi:10.1137/140999980 fatcat:ve2dhxxejjfozlwjfta4zccb6e

Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology [chapter]

Markus Hecher, Patrick Thier, Stefan Woltran
2020 Lecture Notes in Computer Science  
Finally, we provide nested DP algorithms and implementations relying on database technology 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  ... 
doi:10.1007/978-3-030-51825-7_25 fatcat:5cdjcgdqrfgzrckiqrnzdox2qy

Recognition of complex events in open-source web-scale videos

Subhabrata Bhattacharya
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 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  ... 
doi:10.1145/2502081.2502210 dblp:conf/mm/Bhattacharya13 fatcat:nazmpy3ftfau5nqv6d5bmhgjei

Provenance for aggregate queries

Yael Amsterdamer, Daniel Deutch, Val Tannen
2011 Proceedings of the 30th symposium on Principles of database systems of data - PODS '11  
We realize this approach in a concrete construction, first 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.  ... 
doi:10.1145/1989284.1989302 dblp:conf/pods/AmsterdamerDT11 fatcat:g7soooumoravfns24ykag7cgmq

Algorithms for algebraic path properties in concurrent systems of constant treewidth components

Krishnendu Chatterjee, Amir Kafshdar Goharshady, Rasmus Ibsen-Jensen, Andreas Pavlogiannis
2016 SIGPLAN notices  
We study algorithmic questions 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.  ... 
doi:10.1145/2914770.2837624 fatcat:ueekz2sd7jepjpckibhg63xg24
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