Optimal Partition of a Tree with Social Distance
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We study the problem to find a partition of graph G with maximum social welfare based on social distance between vertices in G, called MaxSWP. This problem is known to be NP-hard in general. In this paper, we show that MaxSWP on trees can be solved in time O(Δ^2n), where n is the number of vertices and Δ is the maximum degree of G. Moreover, we show that MaxSWP is NP-hard even for 4-regular graphs.
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