  We consider a general class of binary packing problems with a convex
quadratic knapsack constraint. We prove that these problems are APX-hard to
approximate and present constant-factor approximation algorithms based upon
three different algorithmic techniques: (1) a rounding technique tailored to a
convex relaxation in conjunction with a non-convex relaxation whose
approximation ratio equals the golden ratio; (2) a greedy strategy; (3) a
randomized rounding leading to an approximation algorithm for the more general
case with multiple convex quadratic constraints. We further show that a
combination of the first two strategies 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 the three algorithms for problem instances arising in the
context of real-world gas transport networks.
