AbstractWe consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are$$\mathsf {APX}$$APX-hard to approximate and present constant-factor approximation algorithms based upon two different algorithmic techniques: a rounding technique tailored to a convex relaxation in conjunction with a non-convex relaxation, and a greedy strategy. We further show that a combination of these techniques can be used to yield a monotone algorithm leading to a strategyproof mechanism for a game-theoretic variant of the problem. Finally, we present a computational study of the empirical approximation of these algorithms for problem instances arising in the context of real-world gas transport networks.