Abstract
We present a dynamic programming algorithm for the following problem: Given a tree T=( V, E), a set of q non-negative integer weights w i:V→ N on the nodes, and a threshold R i, i=1,…,q . Partition the vertices of the tree into connected components T 0,…, T k , such that for all i∈{1,…,q}, j∈{0,…,k} ∑ v∈T j w i(v)⩽R i and k is minimal. We show that this problem is hard, if q is unbounded or if T has unbounded maximum degree. In all other cases the running time of the dynamic program has a polynomial worst-case bound.
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