Efficient Pseudopolynomial-Time Algorithm for the Knapsack Problem Leveraging Rectangular Monotone Min-Plus Convolution and Balancing

We present a randomized algorithm for the Knapsack problem that runs in time e O(n + t√pmax), where n is the number of items, t is the knapsack capacity, and pmax is the maximum item profit. This improves upon the previous best known e O(n + t · pmax)-time algorithm.