We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are \(\mathsf {APX}\)-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.

我们考虑一类具有凸二次背包约束的二元包装问题。我们证明这些问题是\(\mathsf {APX}\) -难以近似并提出基于两种不同算法技术的常数因子近似算法：一种针对凸松弛与非凸松弛相结合的舍入技术，和贪婪的策略。我们进一步表明，这些技术的组合可用于产生单调算法，从而为问题的博弈论变体提供策略证明机制。最后，我们针对现实世界天然气运输网络中出现的问题实例，对这些算法的经验近似进行了计算研究。