归纳逻辑程序设计(ILP)是机器学习的一个分支,它依赖于逻辑程序作为一种统一的表示语言来表达例子、背景知识和假设。基于一阶逻辑的ILP具有很强的表示形式,为多关系学习和数据挖掘提供了一种很好的方法。International Conference on Inductive Logic Programming系列始于1991年,是学习结构化或半结构化关系数据的首要国际论坛。最初专注于逻辑程序的归纳,多年来,它大大扩展了研究范围,并欢迎在逻辑学习、多关系数据挖掘、统计关系学习、图形和树挖掘等各个方面作出贡献,学习其他(非命题)基于逻辑的知识表示框架,探索统计学习和其他概率方法的交叉点。官网链接:https://ilp2019.org/

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We study the computational complexity of finding fair allocations of indivisible goods in the setting where a social network on the agents is given. Notions of fairness in this context are "localized", that is, agents are only concerned about the bundles allocated to their neighbors, rather than every other agent in the system. We comprehensively address the computational complexity of finding locally envy-free and Pareto efficient allocations in the setting where the agents have binary valuations for the goods and the underlying social network is modeled by an undirected graph. We study the problem in the framework of parameterized complexity. We show that the problem is computationally intractable even in fairly restricted scenarios, for instance, even when the underlying graph is a path. We show NP-hardness for settings where the graph has only two distinct valuations among the agents. We demonstrate W-hardness with respect to the number of goods or the size of the vertex cover of the underlying graph. We also consider notions of proportionality that respect the structure of the underlying graph and show that two natural versions of this notion have different complexities: allocating according to the notion that accounts for locality to the greatest degree turns out to be computationally intractable, while for other notions, the allocation problem can be modeled as a structured ILP which can be solved efficiently.

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