Balancing a Complete Signed Graph by Changing Minimum Number of Edge Signs
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...
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| Format: | Others |
| Language: | en_US |
| Published: |
2012
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| Online Access: | http://ndltd.ncl.edu.tw/handle/40274147250963197905 |
| Summary: | 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.
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