Abstract
Recently, we proposed a new strategy for designing algorithms, called the searching over separators strategy. We applied this approach to solve some famous NP-Complete problems in subexponential time such as the discrete Euclidean P-median problem, the discrete Euclidean P-center problem, the Euclidean P-center problem and the Euclidean traveling salesperson problem. In this paper, we further extend this strategy to solve two well known NP-Complete problems, the planar partition-into-clique problem (PCliPar) and the planar steiner tree problem (PStTree). We propose \(O(n^{o(\sqrt n )} )\) algorithms for both problems, where n is the number of vertices in the input graph.
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© 1992 Springer-Verlag Berlin Heidelberg
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Hwang, R.Z., Lee, R.C.T. (1992). The application of the searching over separators strategy to solve some NP-complete problems on planar graphs. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_57
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DOI: https://doi.org/10.1007/3-540-56279-6_57
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