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12 '''end else'''
:Then we can get the S-decomposition tree. One thing to note is that we need to '''avoid cycle''' in G" while building it. To do this, for each group of connected edges(and vertices), we assign one represented vertex to all edges(and all vertices) in the group, then the check before each edge addition becomes easy. For example, before we add the new edge E(u, v), we only need to compare the represented vertex of u and that of v, no cycle will occur if the two are different.
* Test each S-prime component to see if it is an interval graph.
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