  We introduce methods to count and enumerate all maximal independent, all
maximum independent sets, and all independent sets in threshold graphs and
k-threshold graphs. Within threshold graphs and k-threshold graphs independent
sets correspond to feasible solutions in related knapsack instances. We give
several characterizations for knapsack instances and multidimensional knapsack
instances which allow an equivalent graph. This allows us to solve special
knapsack instances as well as special multidimensional knapsack instances for
fixed number of dimensions in polynomial time. We also conclude lower bounds on
the number of necessary bins within several bin packing problems.
