A simple $(2+ε)$-approximation for knapsack interdiction
For researchers in combinatorial optimization, this provides a simpler and faster approximation algorithm for a known problem, though it is incremental over the existing PTAS.
The authors present a simpler and faster (2+ε)-approximation algorithm for the knapsack interdiction problem, achieving O(n^3ε^{-1}log(ε^{-1}log∑p_i)) time, and generalize it to a (1+t+ε)-approximation for t-dimensional knapsack interdiction.
In the knapsack interdiction problem, there are $n$ items, each with a non-negative profit, interdiction cost, and packing weight. There is also an interdiction budget and a capacity. The objective is to select a set of items to interdict (delete) subject to the budget which minimizes the maximum profit attainable by packing the remaining items subject to the capacity. We present a $(2+ε)$-approximation running in $O(n^3ε^{-1}\log(ε^{-1}\log\sum_i p_i))$ time. Although a polynomial-time approximation scheme (PTAS) is already known for this problem, our algorithm is considerably simpler and faster. The approach also generalizes naturally to a $(1+t+ε)$-approximation for $t$-dimensional knapsack interdiction with running time $O(n^{t+2}ε^{-1}\log(ε^{-1}\log\sum_i p_i))$.