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}
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\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