图对齐问题中部分恢复的不可能性
Impossibility of Partial Recovery in the Graph Alignment Problem
摘要：
随机图对齐是指恢复具有相关边的两个随机图之间的底层顶点对应关系。这可以被看作是一个普通的情况下，噪声版本的著名的图同构问题。对于相关的Erdös-Rényi模型，我们证明了在稀疏状态下部分恢复的不可能结果，具有常数的平均度和相关性，以及最大可达重叠的一般界。我们的界是紧的无噪声的情况下（图同构问题），我们猜想，它仍然是紧的噪声。我们的证明技术依赖于一个仔细的应用概率方法来建立一个亚临界Erdös-Rényi图的树组件之间的自同构。
英文摘要：
Random graph alignment refers to recovering the underlying vertex correspondence between two random graphs with correlated edges. This can be viewed as an average-case and noisy version of the well-known graph isomorphism problem. For the correlated Erdös-Rényi model, we prove an impossibility result for partial recovery in the sparse regime, with constant average degree and correlation, as well as a general bound on the maximal reachable overlap. Our bound is tight in the noiseless case (the graph isomorphism problem) and we conjecture that it is still tight with noise. Our proof technique relies on a careful application of the probabilistic method to build automorphisms between tree components of a subcritical Erdös-Rényi graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
