发表机构
University of Pisa（比萨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对配置模型无法保持图动力学的问题，提出公平划分可实现性（EP-可实现性）及其近似版本，通过归约到Havel--Hakimi和Gale--Ryser定理求解，实现隐私与效用的可调权衡，并在多个数据集上验证了近似线性时间复杂度和良好性能。
AI 中文摘要
度序列可实现性是配置模型的组合基础，但仅凭度约束并不能确保图动力学的保持。因此，配置模型无法恢复中心性度量，除非这些度量与度序列强相关。为解决此问题，我们引入EP-可实现性，即由公平划分（EP）引发的类似问题：给定一个图的公平划分，判断该划分是否由简单无向无环图实现，并据此构造这样的图。在定义该问题后，我们通过将其归约为与Havel--Hakimi和Gale--Ryser定理相关的子问题来求解。我们还面临用近似公平划分（$\varepsilon$-EP）求解该问题的挑战，从而能够从部分且更具隐私保护性的信息出发重建网络。我们用边重叠评估隐私，并为我们提出的$\varepsilon$-EP-可实现性解决方案推导出该指标的预测器。在Karate、Cora、CiteSeer和PubMed数据集上的实验表明，我们的算法实现了有利且可调的隐私-效用权衡，并与Havel--Hakimi算法、Newman配置模型和随机块模型的结果进行了比较。最后，通过真实数据和随机图，我们证明了我们的算法在边数方面具有近似线性的时间复杂度。
英文摘要
Degree-sequence realizability is the combinatorial basis of configuration models, but degree constraints alone do not ensure the preservation of graph dynamics. Hence, configuration models are unable to recover centrality measures, unless these are strongly correlated with the degree sequence. To address this matter, we introduce EP-realizability, the analogue problem induced by an equitable partition (EP): given the EP of a graph, decide whether the partition is realized by a simple undirected loopless graph and therefore construct such a graph. After defining the problem, we solve it by reducing it to sub-problems related to Havel--Hakimi and the Gale--Ryser theorem. We also face the challenge of solving the problem with an Approximate Equitable Partition ($\varepsilon$-EP), so that it is possible to reconstruct a network starting from partial and more privacy-preserving information. We evaluate privacy with edge overlap, deriving also, for our proposed $\varepsilon$-EP-realizability solution, a predictor for this metric. Experiments on Karate, Cora, CiteSeer and PubMed datasets show that our algorithm achieves a favourable and tunable privacy--utility trade-off, comparing the results with Havel--Hakimi algorithm, Newman's configuration model and a stochastic block model. Finally, both with real data and random graphs, we show that our algorithm has approximately linear time complexity with respect to the number of edges.
