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Incremental complexity of a bi-objective hypergraph transversal problem
[article]

2015
*
arXiv
*
pre-print

Recent applications in computational biology however require to solve

arXiv:1505.06025v1
fatcat:iqmok5x4ajcdhffeun6f5bsuem
*a*generalization*of*this*problem*, that we call*bi*-*objective**transversal**problem*. ... The*hypergraph**transversal**problem*has been intensively studied, from both*a*theoretical and*a*practical point*of*view. ... This implies that if*A*is*of*bounded dimension, min*Problem*2 . 2*Bi*-*objective**hypergraph**transversal**problem*Given*a**hypergraph*G = (V, H) and*a*partition H =*A*∪ B*of*its hyperedges, enumerate the sets ...##
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Incremental Complexity of a Bi-objective Hypergraph Transversal Problem
[chapter]

2015
*
Lecture Notes in Computer Science
*

Recent applications in computational biology however require to solve

doi:10.1007/978-3-319-22177-9_16
fatcat:jghimpm7evgenjqs3sjzlj4pfe
*a*generalization*of*this*problem*, that we call*bi*-*objective**transversal**problem*. ... The*hypergraph**transversal**problem*has been intensively studied, from both*a*theoretical and*a*practical point*of*view. ... Such sets are called*bi*-*objective*minimal*transversals**of*the couple (*A*, B). The collection*of**bi*-*objective*minimal*transversals**of*(*A*, B) is denoted by btr(*A*, B). ...##
###
Constructing Iceberg Lattices from Frequent Closures Using Generators
[chapter]

2008
*
Lecture Notes in Computer Science
*

We propose here to reverse

doi:10.1007/978-3-540-88411-8_15
fatcat:2wekdcdr4ncqxnhwdpun75lwpi
*a*method from the latter field using*a*fundamental property*of**hypergraph*theory. ... Frequent closures (FCIs) and generators (FGs) as well as the precedence relation on FCIs are key components in the definition*of**a*variety*of*association rule bases. ... For instance, an*incremental*algorithm due to Berge [16] computes the T r(G) as the final member*of**a*sequence*of**hypergraphs*, each representing the*transversal**hypergraph**of**a*subgraph*of*G. ...##
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Generating vertices of polyhedra and related problems of monotone generation
[chapter]

2009
*
CRM Proceedings and Lecture notes AMS
*

The well-known vertex enumeration

doi:10.1090/crmp/048/02
fatcat:ucvd4twcsvdtnbdihuyzlnaxdq
*problem*calls for generating all vertices*of**a*polyhedron, given by its description as*a*system*of*linear inequalities. ... Recently,*a*number*of*combinatorial techniques have been developed and applied successfully to*a*large number*of*monotone generation*problems*in different areas. ...*Hypergraph**transversals*. Let H ⊆ 2 V be*a**hypergraph*on*a*finite set*of*vertices V .*A*subset X ⊆ V is said to be*a**transversal**of*H if X ∩ H = ∅ for all H ∈ H. ...##
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A fast compound algorithm for mining generators, closed itemsets, and computing links between equivalence classes

2013
*
Annals of Mathematics and Artificial Intelligence
*

Based on an in-depth analysis

doi:10.1007/s10472-013-9372-8
fatcat:f54qccrlijaennurk2jw3litem
*of*the aforementioned interplay that is rooted in*a*fundamental duality from*hypergraph*theory, we propose*a*new schema that should enable for*a*more parsimonious computation ... The performance*of*Snow-Touch and*of*its closest competitor, Charm-L, were experimentally compared using*a*large variety*of*datasets. ... Yet they scale poorly as FCI miners due to their reliance on*object*-wise computations (e.g. the*incremental*acquisition*of**objects*as in [11] ). ...##
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Generating All Vertices of a Polyhedron Is Hard

2008
*
Discrete & Computational Geometry
*

We show that generating all negative cycles

doi:10.1007/s00454-008-9050-5
fatcat:s5been3h6bcnthbkmvkbhks3m4
*of**a*weighted graph is*a*hard enumeration*problem*, in both the directed and undirected cases. ... Yet, in the case*of*bounded polyhedra the*complexity*remains open. Equivalently the*complexity**of*generating vertices and extreme rays*of*polyhedra remains open. ... It should be added that the best currently known algorithm for the*hypergraph**transversal**problem*runs in*incremental*quasi-polynomial time [22] . ...##
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Generating All Vertices of a Polyhedron Is Hard

2007
*
Discrete & Computational Geometry
*

We show that generating all negative cycles

doi:10.1007/s00454-006-1259-6
fatcat:4oausme7ejfolhbegnti222y74
*of**a*weighted graph is*a*hard enumeration*problem*, in both the directed and undirected cases. ... Yet, in the case*of*bounded polyhedra the*complexity*remains open. Equivalently the*complexity**of*generating vertices and extreme rays*of*polyhedra remains open. ... It should be added that the best currently known algorithm for the*hypergraph**transversal**problem*runs in*incremental*quasi-polynomial time [22] . ...##
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Possible and certain SQL keys

2015
*
Proceedings of the VLDB Endowment
*

Driven by the dominance

doi:10.14778/2809974.2809975
fatcat:ofh72hgibja43fc4ytsotqpbye
*of*the relational model, the requirements*of*modern applications, and the veracity*of*data, we revisit the fundamental notion*of**a*key in relational databases with NULLs. ... Possible keys coincide with the unique constraint*of*SQL, and thus provide*a*semantics for their syntactic definition in the SQL standard. ... This research is partially supported by the Marsden Fund Council from New Zealand Government funding, by the Natural Science Foundation*of*China (Grant No. 61472263) and the Australian Research Council ...##
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Ordered Sets for Data Analysis
[article]

2019
*
arXiv
*
pre-print

That is why we analyze the computational

arXiv:1908.11341v1
fatcat:qusrwndmvrby3hz66clcs2diwa
*complexity**of*algorithms and*problems**of*data analysis. ... On the one hand, data often have*a**complex*structure with natural order on it. ... The*problem**of*computing pseudo-intents is at least as hard as the*problem**of*enumerating all minimal*transversals**of**a**hypergraph*[15] . ...##
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Message-Passing Algorithms and Homology
[article]

2020
*
arXiv
*
pre-print

) and to extend the uniqueness result for acyclic graphs (i.e. trees) to

arXiv:2009.11631v1
fatcat:fppkkjpczvgxvnkbwcxlptc5fq
*a*wider class*of**hypergraphs*. ... Stationary states*of*diffusion are shown to lie at the intersection*of**a*homology class*of*potentials with*a*non-linear constraint surface enforcing consistency*of*the local marginals estimates. ... on the geometric*increment**of*m αβ in equation (6) . ...##
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14th International Symposium on Mathematical Programming

1990
*
Mathematical programming
*

If we use

doi:10.1007/bf01580875
fatcat:3jtclwmntzgjxkqs5uecombdaa
*a*decomposition approach in order to solve*a*minimization*problem*we often get an*objective*function in such*a*w*a*y that its domain dom 6 = n is not given explicitely to us. ...*A*v ariation*of*bundle methods is presented by means*of*which such*a*t ype*of**problems*can be solved.In this variation*a*dynamic polyhedral model*of*dom is generated by means*of*normal vectors.In addition ... First, we clarify the relationship between shellable*hypergraphs*and certain orthogonal expressions*of*Boolean functions. Next, we show that all minimal*transversals**of**a*shellable! ...##
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Spherical harmonic shape descriptors of nodal force demands for quantifying spatial truss connection complexity
[article]

2021
*
arXiv
*
pre-print

We propose

arXiv:2111.10454v1
fatcat:giybubv5bvdhjej5mg3ugigby4
*a*method for quantifying the*complexity**of*spatial truss designs by the variation in nodal force demands. ... We then develop*a*pathway towards reducing*complexity*by clustering nodes with respect to their feature vectors to reduce the number*of*unique connectors for design while minimizing the effects*of*mass ... We analyzed 100 variations*of*the initial example structure to investigate the relationship between nodal*complexity*and structural performance, with the*bi*-*objective*plot shown in Figure 13 . ...##
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The joy of implications, aka pure Horn formulas: Mainly a survey

2017
*
Theoretical Computer Science
*

It is mainly

doi:10.1016/j.tcs.2016.03.018
fatcat:hrz2vsn66rdt3obw42or57h7pa
*a*survey*of*results obtained in the last thirty years, but features*a*few novelties as well. ... We pose four open*problems*to stimulate further research. ... Arguably the single most important fact about general simple*hypergraphs*is [S, p.1377 ] that equality takes place: (20) mtr(mtr(H)) = H The*transversal**hypergraph**problem*, i.e. the*problem**of*calculating ...##
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Subject index volumes 1–200

1999
*
Theoretical Computer Science
*

*of*

*a*

*complex*variable, 614 changeable input size, 164 natural numbers, 29

*problem*size, 57 higher

*complexity*, synthesis

*of*-, 766 uniform

*complexity*, class

*of*-, 332 functions, o-continuous -, ... system

*problem*, 518 satisfiability

*problem*, 2237 strong code, 2111 solvable word

*problem*, 2752

*problems*, 1642 solving

*a*linear system, 3446 communication

*problems*, 2435

*complexity*

*of*-, 2765 ...

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Contents

2012
*
Procedia Engineering
*

and

doi:10.1016/s1877-7058(12)01003-x
fatcat:h3tienvctfgkpkwmhui6bgs4ee
*Transverse*Piezoresistive Coeffi cient on Piezoresistive Pressure Sensor G. ... for Unconstrained Multi-Level Lot-Sizing*Problems*" Y. ...
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