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Covering Properties of Convex Sets
Bulletin of the London Mathematical Society, 1986Partant d'un recouvrement ouvert de certains convexes d'un espace vectoriel topologique séparé, l'A. obtient un recouvrement fermé contenu dans le premier. Le caractère fermé du recouvrement lui permet alors d'utiliser un résultat classique afin d'obtenir une démonstration élégante d'un résultat récent de Ky Fan.
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Solving hard set covering problems
Operations Research Letters, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MANNINO, Carlo, SASSANO, Antonio
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Dimensions of Random Covering Sets
2015In this overview we discuss recent results on dimensional properties of random covering sets.
Järvenpää Esa, Järvenpää Maarit
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New coverings oft-sets with (t + 1)-sets
Journal of Combinatorial Designs, 1999Let \(X\) be a \(v\)-set of points and \({\mathcal B}\) be a family of \(k\)-subsets of \(X\), called blocks. Then the pair \((X,{\mathcal B})\) is called a \(t\)-\((v,k,\lambda)\) covering design if each \(t\)-subset of \(X\) is contained in (or is covered by) at least \(\lambda\) blocks. The minimum size of \({\mathcal B}\) is denoted by \(C_{\lambda}
Nurmela, Kari J. +1 more
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On Capacitated Set Cover Problems
2011Recently, Chakrabarty et al. [5] initiated a systematic study of capacitated set cover problems, and considered the question of how their approximability relates to that of the uncapacitated problem on the same underlying set system. Here, we investigate this connection further and give several results, both positive and negative.
Bansal, N., Krishnaswamy, R., Saha, B.
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1993
Set-covering classification is suitable for classification problems in which the solutions (causes) evoke particular symptoms (effects) — possibly via intermediate states — with a relatively high reliability. In the simplest form the knowledge representation consists of observations, solutions and rules of the form: solution causes observation (S → O).
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Set-covering classification is suitable for classification problems in which the solutions (causes) evoke particular symptoms (effects) — possibly via intermediate states — with a relatively high reliability. In the simplest form the knowledge representation consists of observations, solutions and rules of the form: solution causes observation (S → O).
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Covering analytic sets by families of closed set
Journal of Symbolic Logic, 1994AbstractWe prove that for every familyIof closed subsets of a Polish space eachset can be covered by countably many members ofIor else contains a nonemptyset which cannot be covered by countably many members ofI. We prove an analogous result forκ-Souslin sets and show that ifA#exists for anyA⊂ωω, then the above result is true forsets.
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Covering Numbers in Covering-Based Rough Sets
2011Rough set theory provides a systematic way for rule extraction, attribute reduction and knowledge classification in information systems. Some measurements are important in rough sets. For example, information entropy, knowledge dependency are useful in attribute reduction algorithms.
Shiping Wang, Fan Min, William Zhu
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Information Sciences, 1985
In the paper the least-cost set covering problem \[ LC: \min (c^ Tx\quad | \quad Ax\geq 1,\quad x_ j\in \{0,1\}) \] and its special case, the minimum covering problem \[ MC: \min (1^ Tx\quad | \quad Ax\geq 1,\quad x_ j\in \{0,1\}) \] are dealt with. In the problems above A is the incidence matrix, x is a binary vector to be determined and c is the cost
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In the paper the least-cost set covering problem \[ LC: \min (c^ Tx\quad | \quad Ax\geq 1,\quad x_ j\in \{0,1\}) \] and its special case, the minimum covering problem \[ MC: \min (1^ Tx\quad | \quad Ax\geq 1,\quad x_ j\in \{0,1\}) \] are dealt with. In the problems above A is the incidence matrix, x is a binary vector to be determined and c is the cost
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