| Summary: | 碩士 === 國立東華大學 === 資訊工程學系 === 90 === A graph is chordal if every cycle of length greater than three has a chord. The
treewidth (respectively, minimum ll-in) problem is to nd a chordal supergraph
with the smallest possible maximum clique size (respectively, the minimum number of
additional edges). Similarly, the pathwidth (respectively, interval graph completion)
problem is to nd a interval supergraph with the smallest possible maximum clique
size (respectively, the minimum number of additional edges). Both problems are NPcomplete
on general graphs. They remain NP-complete even for cobipartite graphs,
bipartite graphs and graphs of clique size at most 9. A bipartite permutation graph is
a both bipartite and permutation graph. In this thesis, we present a uni ed approach
to compute the treewidth and minimum ll-in on bipartite permutation graphs in
linear time. The best previous result is O(n2) where n is the number of vertices in
the input graph.
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