The Non-Separating Connector Problem and Exact Algorithms
碩士 === 國立中正大學 === 資訊工程所 === 98 === Consider a connected graph G = (V,E,w) with nonnegative vertex weight and two vertices {s,t} in V . A connected bipartition (V1, V2) of G is that both subgraphs induced by V1 and V2 are connected. If {s,t} in V2 and w(V2) is min- imize, then the vertex set V2 is ca...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2010
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| Online Access: | http://ndltd.ncl.edu.tw/handle/45895505666702790804 |
| Summary: | 碩士 === 國立中正大學 === 資訊工程所 === 98 === Consider a connected graph G = (V,E,w) with nonnegative vertex weight and two vertices {s,t} in V . A connected bipartition (V1, V2) of G is that both subgraphs induced by V1 and V2 are connected. If {s,t} in V2 and w(V2) is min-
imize, then the vertex set V2 is called a non-separating connector, denoted by NSC. In this thesis, we study how to find a NSC in a graph. The bad news is that the NSC problem is NP-hard in the strong sense and can not
be approximated with ratio |V| to the 1-epsilon. Due to NSC problem is NP-hard and it is not easy to find an approximation algorithm with good ratio. A branch
and bound algorithm with two different branching rules are given to find the exact solutions for the NSC problem. We also reduce the NSC problem from general graph to biconnected graph for solving those hard cases which the general branch and bound algorithm does not work efficiently. The experimental results and the comparisons of above algorithm are also shown in this thesis.
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