Technical Note—An Approximate Dynamic Programming Approach to the Incremental Knapsack Problem

Integer packing problems have traditionally been some of the most fundamental and well-studied computational questions in discrete optimization. The paper by Aouad Segev studies incremental knapsack problem, where one wishes to sequentially pack items into a whose capacity expands over finite planning horizon, with objective maximizing time-averaged profits. Although various approximation algorithms were developed under mitigating structural assumptions, obtaining nontrivial performance guarantees for this problem its utmost generality has remained an open question thus far. authors devise first polynomial-time scheme general instances which is strongest guarantee possible given existing hardness results. Their approach synthesizes techniques related approximate dynamic programming, including decompositions, counting arguments, efficient rounding methods, may be broader interest.