An Efficient Algorithm for the Transversal Hypergraph Generation
TL;DR: It is shown that the proposed algorithm operates in a way that rules out regeneration and, thus, its memory requirements are polynomially bounded to the size of the input hypergraph.
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Abstract: The Transversal Hypergraph Generation is the problem of generating, given a hypergraph, the set of its minimal transversals, i.e., the hypergraph whose hyperedges are the minimal hitting sets of the given one. The purpose of this paper is to present an efficient and practical algorithm for solving this problem. We show that the proposed algorithm operates in a way that rules out regeneration and, thus, its memory requirements are polynomially bounded to the size of the input hypergraph. Although no time bound for the algorithm is given, experimental evaluation and comparison with other approaches have shown that it behaves well in practice and it can successfully handle large problem instances.
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Citations
Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints
TL;DR: This paper describes a relationship between satisfiable and unsatisfiable subsets of constraints that is subsequently used as the foundation for MUS extraction algorithms, implemented for Boolean satisfiability constraints.
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Computational aspects of monotone dualization: A brief survey
TL;DR: This paper focuses on the famous paper by Fredman and Khachiyan, which showed that the dualization of monotone disjunctive normal forms is solvable in quasi-polynomial time (and thus most likely not co-NP-hard), as well as on follow-up works.
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The Minimal Hitting Set Generation Problem: Algorithms and Computation
TL;DR: A suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework are provided, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.
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•Proceedings Article
Efficient algorithms for dualizing large-scale hypergraphs
Keisuke Murakami,Takeaki Uno +1 more
- 07 Jan 2013
TL;DR: In this paper, the authors introduce a new set system induced by the minimality condition of the hitting sets, which enables them to use efficient pruning methods and construct time efficient and polynomial space dualization algorithms.
79
Efficient algorithms for dualizing large-scale hypergraphs
Keisuke Murakami,Takeaki Uno +1 more
TL;DR: In this paper, a polynomial space dualization algorithm was proposed to check the minimal hitting set enumeration of a subset family, generation problem for maximal frequent and minimal infrequent sets, and so on.
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