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The third row of Table 2 shows the values of energy function for circular orderings achieved by the MC-Net with the circular ordering obtained by the N-Net as an initial ordering.
The ordering process was simple.
The INITIAL is a greedy algorithm to obtain a circular ordering, namely, the initial circular ordering.
In the first step, we find a circular ordering.
We call function η the energy function, and any circular ordering that minimizes η is called the optimal circular ordering.
The N-Net produces a circular ordering from a distance matrix, then constructs a collection of weighted splits using circular ordering.
Since finding an optimal circular ordering is an NP-hard problem, so we introduce a heuristic algorithm based on the Monte-Carlo method to find optimal circular ordering.
We find that the circular ordering produced by the MC-Net is closer to optimal circular ordering than the N-Net.
Therefore, the MC-Net yields a circular ordering with approximately minimal energy function.
In this case, the circular ordering is said to represent the split system.
In the second step, the splits which are obtained from the circular ordering are weighted.
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