An On Log N Algorithm for the Maximal Planar Subgraph Problem
An On Log N Algorithm for the Maximal Planar Subgraph Problem
Jiazhen Cai
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There- fore we maintain a heap [13] based on bw i values of the unprocessed successors of the tree edge e currently being processed. Since the algorithm is recursive, we actually maintain simultane- ously a heap of unprocessed successors for each tree edge along the path to the currently active tree edge. The total size of all such heaps is 0{m). The initialization of all these heaps takes a total of 0{m) time. When the /owj value of some element in a heap increases, we modify the heap accordin...gly. It is important to note that any two edges in active heaps are unrelated; thus deletion of a single attachment can modify the /owj value of only a single such edge. It follows that the total number of modifications to and deletions from heaps is O (m). The time for the heap operations is 0(}ogn) time per operation, for a total of 0(, m\ogn) time. (Since m
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