An Efficient Algorithm for the Transversal Hypergraph Generation

Kavvadias, Dimitris J.; Stavropoulos, Elias C.

doi:10.7155/jgaa.00107

Cited by 57 publications

(69 citation statements)

References 35 publications

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“…This part requires all of D i memory, thus we need to perform a breadth-first search. Kavadias and Stavropoulos [8,9] proposed a depth-first version of this algorithm. According to the hitting sets generation rule, each hitting set in F i is uniquely generated from a hitting set of F i−1 .…”

Section: Existing Algorithmsmentioning

confidence: 99%

“…Kavvadias and Stavropoulos's algorithm (KS algorithm) [8,9] embodies two ideas; unifying the nodes contained in the same hyperedges and depth-first search. These ideas help to reduce the number of intermediate hitting sets and memory usage.…”

Section: Related Workmentioning

confidence: 99%

“…We alleviate this disadvantage by using a depth-first search algorithm with the use of the new minimality check algorithm explained below. The algorithm proposed in [8,9] uses a depth-first search, but its minimality check takes a long time on large hypergraphs. -minimality check: The time for the minimality check in a breadth-first search is short when the hitting sets to be checked are small on average, but will be long for larger hitting sets (such as size 20 or larger).…”

Section: Introductionmentioning

confidence: 99%

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Efficient algorithms for dualizing large-scale hypergraphs

Murakami

Uno

2014

Discrete Applied Mathematics

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Abstract. A hypergraph F is a set family defined on vertex set V . The dual of F is the set of minimal subsets H of V such that F ∩H = ∅ for any F ∈ F. The computation of the dual is equivalent to many problems, such as minimal hitting set enumeration of a subset family, minimal set cover enumeration, and the enumeration of hypergraph transversals. Although many algorithms have been proposed for solving the problem, to the best of our knowledge, none of them can work on large-scale input with a large number of output minimal hitting sets. This paper focuses on developing time-and space-efficient algorithms for solving the problem. We propose two new algorithms with new search methods, new pruning methods, and fast techniques for the minimality check. The computational experiments show that our algorithms are quite fast even for large-scale input for which existing algorithms do not terminate in a practical time.

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Section: Existing Algorithmsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient algorithms for dualizing large-scale hypergraphs

Murakami

Uno

2014

Discrete Applied Mathematics

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“…∧ C j−1 , and simplifying the DNF's using the absorption law (i.e., the identity x ∨ (x ∧ y) = x for all Boolean x, y) whenever possible (see Figure 1). We remark that many practical algorithms for monotone dualization are obtained from the left-to-right multiplication by putting several heuristic ideas (see e.g., [2,10,23,35]). …”

Section: Introductionmentioning

confidence: 99%

On Berge Multiplication for Monotone Boolean Dualization

Boros

Elbassioni

Makino

2008

Automata, Languages and Programming

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Abstract. Given the prime CNF representation φ of a monotone Boolean function f : {0, 1} n → {0, 1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f . A very simple method (called Berge multiplication [3, Page 52-53]) works by multiplying out the clauses of φ from left to right in some order, simplifying whenever possible using the absorption law. We show that for any monotone CNF φ, Berge multiplication can be done in subexponential time, and for many interesting subclasses of monotone CNF's such as CNF's with bounded size, bounded degree, bounded intersection, bounded conformality, and read-once formula, it can be done in polynomial or quasi-polynomial time.

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“…Thus, we adopt a deep first strategy for computing transversals as described in [13]. The idea is to compute a transversal of the partial hypergraph and then add the next hyperedge to it.…”

Section: Definition 8 a Set T ⊂ σ Is A Transversal Of H If For Each mentioning

confidence: 99%

Semantic Composition of Lecture Subparts for a Personalized e-Learning

Karam

Linckels

Meinel

Lecture Notes in Computer Science

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Abstract. In this paper we propose an algorithm for personalized learning based on a user's query and a repository of lecture subparts -i.e., learning objects-both are described in a subset of OWL-DL. It works in two steps. First, it retrieves lecture subparts that cover as much as possible the user's query. The solution is based on the concept covering problem for which we present a modified algorithm. Second, an appropriate sequence of lecture subparts is generated. Indeed, the different lecture subparts are only reachable when a given prerequisite is fulfilled, i.e., the learner must have a minimal background knowledge to be able to assimilate the requested learning object. Therefore, our algorithm takes into account the user's knowledge to generate a personalized lecture composition and suggests a flow of learning objects to the user.

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An Efficient Algorithm for the Transversal Hypergraph Generation

Cited by 57 publications

References 35 publications

Efficient algorithms for dualizing large-scale hypergraphs

Efficient algorithms for dualizing large-scale hypergraphs

On Berge Multiplication for Monotone Boolean Dualization

Semantic Composition of Lecture Subparts for a Personalized e-Learning

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