An algorithm for solving minimum edge-ranking spanning tree problem on partial k-trees - Sultana, Razia (Daffodil International University Journal of Science and Technology, 2010)
An edge-ranking of a graph G is a labeling of its edges with positive integers such that every path between two edges with the same label i contains an intermediate edge with label j>i. The minimum edge-ranking spanning tree problem is to find a spanning tree of a graph G whose edge-ranking needs least number of ranks. In this paper, we present an algorithm to solve the minimum edge-ranking spanning tree problem on a partial k-tree G in O(n2Δ(k+1)+2 Δk(k+1)+2 log2 k(k+1)+2n) time, where n is the number of vertices, Δ is the maximum vertex degree of the graph G and k is bounded by a constant value. Keywords: Algorithm, partial k-trees, edge-ranking, spanning tree. DOI: 10.3329/diujst.v4i1.4347 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.1-8