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A Polynomial Time Approximation Scheme for Enormous Euclidean Minimum Spanning Tree Problem  

Kim, In-Bum (School of Information Technology, Kimpo College)
Publication Information
Journal of the Institute of Electronics Engineers of Korea CI / v.48, no.5, 2011 , pp. 64-73 More about this Journal
Abstract
The problem of Euclidean minimum spanning tree (EMST) is to connect given nodes in a plane with minimum cost. There are many algorithms for the polynomial time problem as EMST. However, for numerous nodes, the algorithms consume an enormous amount of time to find an optimal solution. In this paper, an approximation scheme using a polynomial time approximation scheme (PTAS) algorithm with dividing and parallel processing for the problem is suggested. This scheme enables to construct a large, approximate EMST within a short duration. Although initially devised for the non-polynomial problem, we employ naive PTAS to construct a vast EMST with dynamic programming. In an experiment, the approximate EMST constructed by the proposed scheme with 15,000 input terminal nodes and 16 partition cells shows 89% and 99% saving in execution time for the serial processing and parallel processing methods, respectively. Therefore, our scheme can be applied to obtain an approximate EMST quickly for numerous input terminal nodes.
Keywords
Euclidean Minimum Spanning Tree; Polynomial Time Approximation Scheme; Portal;
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Times Cited By KSCI : 1  (Citation Analysis)
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