Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
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Efficient Construction of Euclidean Steiner Minimum Tree Using Combination of Delaunay Triangulation and Minimum Spanning Tree

들로네 삼각망과 최소신장트리를 결합한 효율적인 유클리드 스타이너 최소트리 생성

  • Kim, Inbum (Dept. of Internet Information, Kimpo College)
  • Received : 2013.11.15
  • Accepted : 2013.12.14
  • Published : 2014.01.29
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Abstract

As Steiner minimum tree building belongs to NP-Complete problem domain, heuristics for the problem ask for immense amount execution time and computations in numerous inputs. In this paper, we propose an efficient mechanism of euclidean Steiner minimum tree construction for numerous inputs using combination of Delaunay triangulation and Prim's minimum spanning tree algorithm. Trees built by proposed mechanism are compared respectively with the Prim's minimum spanning tree and minimums spanning tree based Steiner minimum tree. For 30,000 input nodes, Steiner minimum tree by proposed mechanism shows about 2.1% tree length less and 138.2% execution time more than minimum spanning tree, and does about 0.013% tree length less and 18.9% execution time less than minimum spanning tree based Steiner minimum tree in experimental results. Therefore the proposed mechanism can work moderately well to many useful applications where execution time is not critical but reduction of tree length is a key factor.

스타이너 트리의 생성은 NP-Complete 영역에 속하므로, 이것을 위한 휴리스틱들은, 다수의 입력 노드에 대해서 많은 시간과 계산을 요구한다. 본 논문에서는 많은 입력노드에 대해, 들로네 삼각망과 Prim의 최소신장트리를 결합한 효과적인 유클리드 스타이너 최소트리 구성방법을 제안한다. 이 방법은 Prim의 최소신장트리와 최소신장트리기반 스타이너 트리와 각각 비교 분석되었다. 제안된 방법은 30,000개의 입력노드에 대해 최소신장트리에 비해 연결 길이는 2.1% 감소, 실행시간은 138.2% 증가하였고, 최소신장트리기반 스타이너최소트리에 비해 실행시간 18.9% 감소, 연결 길이 0.013% 감소의 실험결과를 보였다. 따라서 본 연구의 제안방법은 실행시간이 주요 요인이 되지 않는 환경에서 연결 길이를 단축해야 할 응용에 잘 적용될 수 있을 것이다.

Keywords

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