I am looking for a heuristic that solves a budgeted variant of the max cut problem.
Given a graph $G = (V, E)$, if the original problem is to find a partition of $V$ into two subsets $A$ and $B$ where $A \cap B = \emptyset$ such that the size of the cut set $\{(u, v) \in E \mid u \in A, v \in B\}$ is maximised, then I define the budgeted variant of this problem to be almost identical except with the constraint that $|A| = b $ for some $b \in \mathbb{N}$, i.e. find the $b$ nodes in $V$ that maximise the cut set.
Is this a well studied problem?
I have found some papers that seem related to this, e.g. [1], [2] and [3] but I am finding them difficult to read and relate back to the max cut problem. For instance [1] and [2] discuss auctions which I am finding quite confusing. [3] seems to more directly address it but is from 2001, so I am curious whether there are any more recent papers, potentially with better run time complexity, etc.
Does anyone know if there is a paper that addresses this budgeted max cut problem directly and provides a heuristic for solving it?