稀疏化$k$步随机游动的密度无关算法
Density Independent Algorithms for Sparsifying $k$-Step Random Walks
摘要：
我们给更快的算法产生稀疏近似的转移矩阵的$k$步随机游动无向，加权图。这些转移矩阵也形成图，并且在各种图算法中作为中间对象出现。我们的改进是基于更好地理解的过程中，采样这样的散步，以及这些采样过程的关键权重更严格的界限。在具有$n$顶点和$m$边的图上，我们的算法在大约$m + n \log^4{n}$时间内产生一个具有大约$n\log{n}$边的图，该图近似于$k$步随机游动图.为了获得这个运行时的界限，我们还重新审视“密度无关”算法稀疏化图形的运行时开销只表示在顶点的数量。
英文摘要：
We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of graph algorithms. Our improvements are based on a better understanding of processes that sample such walks, as well as tighter bounds on key weights underlying these sampling processes. On a graph with $n$ vertices and $m$ edges, our algorithm produces a graph with about $n\log{n}$ edges that approximates the $k$-step random walk graph in about $m + n \log^4{n}$ time. In order to obtain this runtime bound, we also revisit "density independent" algorithms for sparsifying graphs whose runtime overhead is expressed only in terms of the number of vertices.
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。
