Already 30 years ago, Chvátal has shown that some instances of the zero-one knapsack problem cannot be solved in polynomial time using a particular type of branch-and-bound algorithms based on relaxations oflinear programs together with some rudimentary cutting-plane arguments as bounding rules. We extend this result by proving an exponential lower bound in a more general class of branch-and-bound and dynamic programming algorithms which are allowed to use memoization and arbitrarily powerful bound rules to detect and remove subproblems leading to no optimal solution. © 2011 Elsevier B.V. All rights reserved.
Jukna, S., & Schnitger, G. (2011). Yet harder knapsack problems. Theoretical Computer Science, 412(45), 6351–6358. https://doi.org/10.1016/j.tcs.2011.07.003