Approximating the minimum degree spanning tree to within one from the optimal degree
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
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STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
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SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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The minimum degree spanning tree problem has been studied extensively. In this paper, we present a polynomial time algorithm for the minimum degree spanning tree problem on directed acyclic graphs. The algorithm starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree. We can prove the algorithm must reduce a vertex of the maximum degree for each phase, and finally result in an optimal tree. The algorithm terminates in O(mnlogn) time, where m and n are the number of edges and vertices respectively.