On the Minimum Ranking Spanning Tree Problem

• Main Authors: Jui-Yuan Chang, 張睿元
• Other Authors: Sheng-Lung Peng
• Format: Others
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/10126879535203296845

博士 === 國立東華大學 === 資訊工程學系 === 103 === An edge (respectively, vertex) ranking of a graph G is a labeling of edges (respectively, vertex) of G with positive integers such that every path in $G$ between any two edges (respectively, vertices) of the same label i contains at least one edge (respectively, vertex) on the path with label j>i. The minimum edge (respectively, vertex) ranking problem on $G$ is to find an edge (respectively, vertex) ranking whose largest label is the smallest among all possible edge (respectively, vertex) rankings of G. The minimum edge (respectively, vertex) ranking spanning tree problem on G is to find a spanning tree T of G such that the minimum edge (respectively, vertex) ranking of T is the minimum among all possible spanning trees of G. In this thesis, we study the minimum vertex ranking spanning tree problem and the minimum edge ranking spanning tree problem on some classes of graphs. A linear-time algorithm for solving the minimum vertex ranking spanning tree problem on permutation graphs is proposed. Moreover, two polynomial-time algorithms are proposed for solving the minimum edge ranking spanning tree problem on interval graphs and block graphs respectively.