  Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial
optimization. Recently there has been a growing interest in understanding the
best possible pseudopolynomial running times for these problems with respect to
various parameters.
  In this paper we focus on the maximum item size $s$ and the maximum item
value $v$. We give algorithms that run in time $O(n + s^3)$ and $O(n + v^3)$
for the Knapsack problem, and in time $\tilde{O}(n + s^{5/3})$ for the Subset
Sum problem.
  Our algorithms work for the more general problem variants with
multiplicities, where each input item comes with a (binary encoded)
multiplicity, which succinctly describes how many times the item appears in the
instance. In these variants $n$ denotes the (possibly much smaller) number of
distinct items.
  Our results follow from combining and optimizing several diverse lines of
research, notably proximity arguments for integer programming due to Eisenbrand
and Weismantel (TALG 2019), fast structured $(\min,+)$-convolution by Kellerer
and Pferschy (J. Comb. Optim. 2004), and additive combinatorics methods
originating from Galil and Margalit (SICOMP 1991).
