knapsack-problem – Tarik Billa

0/1 knapsack with dependent item weight?

December 17, 2023 by Tarik

Could you not have items a, b, c, bc, d and e? Possibly with a constraint that b and bc can’t be both in the knapsack and similarly so with c and bc? My understanding is that that would be a correct solution since any solution that has b and c can be improved by … Read more

Why is the knapsack problem pseudo-polynomial?

December 27, 2022 by Tarik

The running time is O(NW) for an unbounded knapsack problem with N items and knapsack of size W. W is not polynomial in the length of the input though, which is what makes it pseudo-polynomial. Consider W = 1,000,000,000,000. It only takes 40 bits to represent this number, so input size = 40, but the … Read more