Computation Theory and Mathematics searching 1992-01-01 Euclidean p algorithm applications 1992 input graph vertices discrete Euclidean P number of vertices planar partition famous NP-complete problem strategies NP-complete problem planar steiner tree problem clique problem 2022-01-01T19:12 new strategy graph false paper chapters The application of the searching over separators strategy to solve some NP-complete problems on planar graphs salesperson problem https://doi.org/10.1007/3-540-56279-6_57 chapter planar graphs subexponential time time number en approach median problem problem separators strategy 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$O(n^{o(\sqrt n )} )$$ \end{document} algorithms for both problems, where n is the number of vertices in the input graph. Steiner tree problem partition Euclidean https://scigraph.springernature.com/explorer/license/ tree problem center problem 51-60 Information and Computing Sciences Hwang R. Z. Lee R. C. T. 978-3-540-47501-9 978-3-540-56279-5 Algorithms and Computation Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, 30043, Republic of China Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, 30043, Republic of China Inagaki Yasuyoshi dimensions_id pub.1013432288 Masafumi Yamashita doi 10.1007/3-540-56279-6_57 Nishizeki Takao Kazuo Iwama Springer Nature Springer Nature - SN SciGraph project Ibaraki Toshihide