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.
60
References
•Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
Michael Randolph Garey,David S. Johnson +1 more
- 01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
A theory of diagnosis from first principles
TL;DR: The theory accommodates diagnostic reasoning in a wide variety of practical settings, including digital and analogue circuits, medicine, and database updates, and reveals close connections between diagnostic reasoning and nonmonotonic reasoning.
3.2K
•Book
Hypergraphs: Combinatorics of Finite Sets
Claude Berge
- 11 Jul 2011
TL;DR: This chapter discusses Hypergraphs Generalising Bipartite Graphs, which are a collection of hypergraphs designed to solve the problem of Uniform Colourings in Matroids, and some of the properties of these graphs.
1K