Abstract
Let \(\mathcal{C}\) be an n-dimensional integral box, and π be a monotone property defined over the elements of \(\mathcal{C}\). We consider the problems of incrementally generating jointly the families \(\mathcal{F}_{\pi}\) and \(\mathcal{G}_{\pi}\) of all minimal subsets satisfying property π and all maximal subsets not satisfying property π, when π is given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time. In this paper, we present an efficient implementation of this procedure. We present experimental results to evaluate our implementation for a number of interesting monotone properties π.
This research was supported by the National Science Foundation (Grant IIS-0118635). 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. (2004). An Efficient Implementation of a Joint Generation Algorithm. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_9
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DOI: https://doi.org/10.1007/978-3-540-24838-5_9
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