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

Ricardo Andrade, Etienne Birmelé, Marie-France Sagot
2015 arXiv   pre-print
Recent applications in computational biology however require to solve 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  ... 
arXiv:1505.06025v1 fatcat:iqmok5x4ajcdhffeun6f5bsuem

Incremental Complexity of a Bi-objective Hypergraph Transversal Problem [chapter]

Ricardo Andrade, Etienne Birmelé, Arnaud Mary, Thomas Picchetti, Marie-France Sagot
2015 Lecture Notes in Computer Science  
Recent applications in computational biology however require to solve 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).  ... 
doi:10.1007/978-3-319-22177-9_16 fatcat:jghimpm7evgenjqs3sjzlj4pfe

Constructing Iceberg Lattices from Frequent Closures Using Generators [chapter]

Laszlo Szathmary, Petko Valtchev, Amedeo Napoli, Robert Godin
2008 Lecture Notes in Computer Science  
We propose here to reverse 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.  ... 
doi:10.1007/978-3-540-88411-8_15 fatcat:2wekdcdr4ncqxnhwdpun75lwpi

Generating vertices of polyhedra and related problems of monotone generation [chapter]

Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Kazuhisa Makino
2009 CRM Proceedings and Lecture notes AMS  
The well-known vertex enumeration 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.  ... 
doi:10.1090/crmp/048/02 fatcat:ucvd4twcsvdtnbdihuyzlnaxdq

A fast compound algorithm for mining generators, closed itemsets, and computing links between equivalence classes

Laszlo Szathmary, Petko Valtchev, Amedeo Napoli, Robert Godin, Alix Boc, Vladimir Makarenkov
2013 Annals of Mathematics and Artificial Intelligence  
Based on an in-depth analysis 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] ).  ... 
doi:10.1007/s10472-013-9372-8 fatcat:f54qccrlijaennurk2jw3litem

Generating All Vertices of a Polyhedron Is Hard

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich
2008 Discrete & Computational Geometry  
We show that generating all negative cycles 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] .  ... 
doi:10.1007/s00454-008-9050-5 fatcat:s5been3h6bcnthbkmvkbhks3m4

Generating All Vertices of a Polyhedron Is Hard

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich
2007 Discrete & Computational Geometry  
We show that generating all negative cycles 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] .  ... 
doi:10.1007/s00454-006-1259-6 fatcat:4oausme7ejfolhbegnti222y74

Possible and certain SQL keys

Henning Köhler, Sebastian Link, Xiaofang Zhou
2015 Proceedings of the VLDB Endowment  
Driven by the dominance 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  ... 
doi:10.14778/2809974.2809975 fatcat:ofh72hgibja43fc4ytsotqpbye

Ordered Sets for Data Analysis [article]

Sergei O. Kuznetsov
2019 arXiv   pre-print
That is why we analyze the computational 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] .  ... 
arXiv:1908.11341v1 fatcat:qusrwndmvrby3hz66clcs2diwa

Message-Passing Algorithms and Homology [article]

Olivier Peltre
2020 arXiv   pre-print
) and to extend the uniqueness result for acyclic graphs (i.e. trees) to 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) .  ... 
arXiv:2009.11631v1 fatcat:fppkkjpczvgxvnkbwcxlptc5fq

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
If we use 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!  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Spherical harmonic shape descriptors of nodal force demands for quantifying spatial truss connection complexity [article]

Keith J. Lee, Renaud Danhaive, Caitlin T. Mueller
2021 arXiv   pre-print
We propose 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 .  ... 
arXiv:2111.10454v1 fatcat:giybubv5bvdhjej5mg3ugigby4

The joy of implications, aka pure Horn formulas: Mainly a survey

Marcel Wild
2017 Theoretical Computer Science  
It is mainly 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  ... 
doi:10.1016/j.tcs.2016.03.018 fatcat:hrz2vsn66rdt3obw42or57h7pa

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  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Contents

2012 Procedia Engineering  
and Transverse Piezoresistive Coeffi cient on Piezoresistive Pressure Sensor G.  ...  for Unconstrained Multi-Level Lot-Sizing Problems" Y.  ... 
doi:10.1016/s1877-7058(12)01003-x fatcat:h3tienvctfgkpkwmhui6bgs4ee
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