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- W4297780810 abstract "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 $nlog{n}$ 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." @default.
- W4297780810 created "2022-10-01" @default.
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- W4297780810 date "2017-02-20" @default.
- W4297780810 modified "2023-09-24" @default.
- W4297780810 title "Density Independent Algorithms for Sparsifying $k$-Step Random Walks" @default.
- W4297780810 doi "https://doi.org/10.48550/arxiv.1702.06110" @default.
- W4297780810 hasPublicationYear "2017" @default.
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