In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that , where is the maximal degree and m is the number of edges, the algorithm runs in expected time O(m). Our algorithm significantly improves the previously most efficient uniform sampler, which runs in expected time for the same family of degree sequences. Our method uses a novel ingredient which progressively relaxes restrictions on an object being generated uniformly at random, and we use this to give fast algorithms for uniform sampling of graphs with other degree sequences as well. Using the same method, we also obtain algorithms with expected run time which is (i) linear for power-law degree sequences in cases where the previous best was O(n^4.081), and (ii) O(nd + d⁴) for d-regular graphs when , where the previous best was O(nd³).

中文翻译：

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具有给定度数序列的随机图的快速均匀生成

在本文中，我们提供了一种算法，该算法可以随机均匀地生成具有给定度数序列的图。假设，其中是最大度数，m是边数，则算法在预期时间O ( m ) 内运行。我们的算法显着改进了以前最高效的均匀采样器，它在预期时间内运行对于相同的学位序列族。我们的方法使用了一种新的成分，它逐渐放宽对随机均匀生成的对象的限制，并且我们使用它来提供快速算法，用于对具有其他度数序列的图进行均匀采样。使用相同的方法，我们还获得了具有预期运行时间的算法，该算法具有 (i) 在先前最佳为O ( n ^4.081 ) 和 (ii) O ( nd  +  d ⁴ ) 的情况下，^幂律度序列的线性d -正则图 when ，其中前一个最好的是O ( nd ³ )。