We are given $n$ tasks and $m$ resources. Each task $i$ requires a set $S_i$ of resources to be active, and each resource can be used by at most one task. The Resource Allocation problem asks: given $S_1, \ldots, S_n$, and an integer $k$, whether it is possible to allocate the resources to the tasks so that at least $k$ tasks are active. Give a polynomial-time reduction from Independent Set to Resource Allocation
I am not sure how to construct the reduction. The difficulty I am having is the solver looks like a solver for a bipartite graph problem but we do not necessarily get a bipartite graph. Thank you!