We consider the classical problem of allocating indivisible resources among agents in an envy-free (and, where applicable, proportional) way. Recently, the basic model was enriched by introducing the concept of a social network which allows to capture situations where agents might not have full information about the allocation of all resources. We initiate the study of the parameterized complexity of these resource allocation problems by considering natural parameters which capture structural properties of the network and similarities between agents and resources. In particular, we show that even very general fragments of the considered problems become tractable as long as the social network has constant treewidth or clique-width. We complement our results with matching lower bounds which show that our algorithms cannot be substantially improved.

我们考虑以无嫉妒（并且在适用的情况下按比例）方式在代理之间分配不可分割的资源的经典问题。最近，通过引入社交网络的概念丰富了基本模型，它允许捕获代理可能没有关于所有资源分配的完整信息的情况。我们通过考虑捕获网络结构特性的自然参数以及代理和资源之间的相似性，开始研究这些资源分配问题的参数化复杂性。特别是，我们表明，只要社交网络具有恒定的树宽或集团宽度，即使是所考虑问题的非常一般的片段也变得易于处理。我们用匹配的下限来补充我们的结果，这表明我们的算法无法得到实质性的改进。