Balancing a Complete Signed Graph by Changing Minimum Number of Edge Signs

• Main Authors: Po-Sun Wei, 魏伯珊
• Other Authors: Bang Ye Wu
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/40274147250963197905

碩士 === 國立中正大學 === 資訊工程研究所 === 100 === A signed graph is a simple undirected graph G = (V,E) in which each edge is labeled by a sign either +1 or -1. A signed graph is balanced if every cycle has even numbers of negative edges. In this thesis we study the problem of balancing a complete signed graph by changing minimum number of edge signs. We give a simple algorithm for nding a solution agreeing one half of the edges. We also design a branch-and-bound algorithm and show the worst-case time complexity is O(n · 2^min{n,k}), in which n = |V| and k is the minimum number of changing edges. By experiments on random graphs, we show that our branch-and-bound algorithm is much faster than a trivial one.