Abstract
Given a finite set V, and a hypergraph \(\mathcal{H} \subseteq 2^V\), the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for \(\mathcal{H}\). This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan (1996) gave an incremental quasi-polynomial time algorithm for solving the hypergraph transversal problem [9]. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same bound on the running time as in [9], practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the algorithm in [9] can be used to give a stronger bound on the running time.
This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The third author is also grateful for the partial support by DIMACS, the National Science Foundation’s Center for Discrete Mathematics and Theoretical Computer Science.
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Boros, E., Elbassioni, K., Gurvich, V., Khachiyan, L. (2003). An Efficient Implementation of a Quasi-polynomial Algorithm for Generating Hypergraph Transversals. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_51
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DOI: https://doi.org/10.1007/978-3-540-39658-1_51
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