Sharing infrastructure between many users is often advantageous, however finding a fair and reasonable way to allocate its cost between its users can be challenging. This is particularly true for LPWANs, a popular Internet of Things solution for wirelessly connecting devices to the internet. We study cost-allocation of LPWANS using a covering integer program. Standard cost-allocation methods are inapplicable in this model, because the integrality gap of its natural LP-relaxation is unbounded. We overcome this challenge by strengthening the natural LP with knapsack-cover inequalities. Our main result is proving that all dual-feasible solutions to the strengthened LP produce cost-allocations that satisfy the core property. This reduces the problem of finding a cost-allocation to that of finding a strengthened-LP-relative approximation algorithm. Existing algorithms imply improved cost-recovery ratios for families of sparse CIP instances. Finally, we show that the strengthened formulation simplifies and improves the analysis of a cross-monotone cost-allocation mechanism as well.

翻译：基础设施的共享通常对多用户有利，但如何公平合理地在其用户间分配成本却颇具挑战性，对于低功耗广域网（LPWAN）这一将设备无线连接至互联网的流行物联网解决方案而言尤其如此。我们利用覆盖整数规划研究LPWAN的成本分摊问题。由于该模型自然线性松弛的整数性间隙无界，标准成本分摊方法在此不适用。我们通过引入背包覆盖不等式强化该自然线性规划来克服这一挑战。主要结论是：强化线性规划的所有对偶可行解都能产生满足核心性质的成本分摊方案。这便将成本分摊问题归结为寻找基于强化线性规划的近似比算法问题。现有算法可改进稀疏覆盖整数规划实例族的成本回收率。最后，我们证明该强化公式同样简化并改进了交叉单调成本分摊机制的分析。