Title of article :
A polynomial algorithm to compute the minimum degree spanning trees of directed acyclic graphs with applications to the broadcast problem Original Research Article
Author/Authors :
Guohui Yao، نويسنده , , Daming Zhu، نويسنده , , Hengwu Li، نويسنده , , Shaohan Ma، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Pages :
9
From page :
3951
To page :
3959
Abstract :
In this paper, we focus on the directed minimum degree spanning tree problem and the minimum time broadcast problem. Firstly, we propose a polynomial time algorithm for the minimum degree spanning tree problem in directed acyclic graphs. The algorithm starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree. We can prove that the algorithm must reduce a vertex of the maximum degree for each phase, and finally result in an optimal tree. The algorithm terminates in image time, where m and n are the numbers of edges and vertices of the graph, respectively. Moreover, we apply the new algorithm to the minimum time broadcast problem. Two consequences for directed acyclic graphs are: (1) the problem under the vertex-disjoint paths mode can be approximated within a factor of image of the optimum in image-time; (2) the problem under the edge-disjoint paths mode can be approximated within a factor of image of the optimum in image-time, where image is the minimum k such that there is a spanning tree of the graph with maximum degree k.
Keywords :
Minimum time broadcast , Spanning tree , Directed acyclic graph , Algorithm
Journal title :
Discrete Mathematics
Serial Year :
2008
Journal title :
Discrete Mathematics
Record number :
947004
Link To Document :
بازگشت