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http://dx.doi.org/10.9708/jksci.2012.17.7.087

Fast Construction of Three Dimensional Steiner Minimum Tree Using PTAS  

Kim, In-Bum (Dept. of Internet Information, Kimpo College)
Publication Information
Journal of the Korea Society of Computer and Information / v.17, no.7, 2012 , pp. 87-95 More about this Journal
Abstract
In this paper, PTAS three-dimensional Steiner minimum tree connecting numerous input nodes rapidly in 3D space is proposed. Steiner minimum tree problem belongs to NP problem domain, and when properly devised heuristic introduces, it is generally superior to other algorithms as minimum spanning tree affiliated with P problem domain. But when the number of input nodes is very large, the problem requires excessive execution time. In this paper, a method using PTAS is proposed to solve the difficulty. In experiments for 70,000 input nodes in 3D space, the tree produced by the proposed 8 space partitioned PTAS method reduced 86.88% execution time, compared with the tree by naive 3D steiner minimum tree method, though increased 0.81% tree length. This affirms the proposed method can work well for applications that many nodes of three dimensions are need to connect swifty, enduring slight increase of tree length.
Keywords
PTAS; Steiner Minimum Tree; Minimum Spanning Tree; 3-Dimensional Space; Execution Time;
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Times Cited By KSCI : 1  (Citation Analysis)
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