Consider the following problem:Given an integer $k$ and a vertex-weighted graph $G=(V,E)$, find a  partition of $V$ into $V_1,\ldots,V_k$ such that each subgraph induced by $V_i$ is connected, and such that $\max_i w(V_i)$ is  minimized, where $w(V_i)$ is the total weight of the vertices in  $V_i$.It can be easily seen that this problem is NP-complete. For hardness, note that we can solve Partition by using a complete graph.Questions: Does this problem have a standard name? Are there any papers that study this problem, or maybe slight variations of it? Is the problem still hard for sparse graphs? I am particularly interested in references that could lead to an implementation with good performance in practice.
Does the problem partition a vertex-weighted graph into $k$ balanced connected parts have a standard name?
graph theory;graph algorithms;co.combinatorics;np hardness;optimization