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

Korean Society of Computer Information (한국컴퓨터정보학회)
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A Degree-Constrained Minimum Spanning Tree Algorithm Using k-opt

k-opt를 적용한 차수 제약 최소신장트리 알고리즘

  • Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
  • 이상운 (강릉원주대학교 멀티미디어공학과)
  • Received : 2015.02.11
  • Accepted : 2015.04.10
  • Published : 2015.05.30
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Abstract

The degree-constrained minimum spanning tree (d-MST) problem is considered NP-complete for no exact solution-yielding polynomial algorithm has been proposed to. One thus has to resort to an heuristic approximate algorithm to obtain an optimal solution to this problem. This paper therefore presents a polynomial time algorithm which obtains an intial solution to the d-MST with the help of Kruskal's algorithm and performs k-opt on the initial solution obtained so as to derive the final optimal solution. When tested on 4 graphs, the algorithm has successfully obtained the optimal solutions.

방향 가중 그래프의 차수제약 최소신장트리 (degree-constrained minimum spanning tree, d-MST) 문제는 정확한 해를 구하는 다항시간 알고리즘이 존재하지 않아 NP-완전 문제로 알려져 왔다. 따라서 휴리스틱한 근사 알고리즘을 적용하여 최적 해를 구하고 있다. 본 논문은 차수와 사이클을 검증하는 Kruskal 알고리즘으로 d-MST의 초기 해를 구하고, d-MST의 초기 해에 대해 k-opt를 수행하여 최적 해를 구하는 다항시간 알고리즘을 제안하였다. 제안된 알고리즘을 4개의 그래프에 적용한 결과 2-MST까지 최적 해를 구할 수 있었다.

Keywords

References

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