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- W1585144678 abstract "In this paper, we make use of the Metropolis-type walks due to Nonaka et al. (2010) to provide a faster solution to the $S$-$T$-connectivity problem in undirected graphs (USTCON). As our main result, we propose a family of randomized algorithms for USTCON which achieves a time-space product of $Scdot T = tilde O(n^2)$ in graphs with $n$ nodes and $m$ edges (where the $tilde O$-notation disregards poly-logarithmic terms). This improves the previously best trade-off of $tilde O(n m)$, due to Feige (1995). Our algorithm consists in deploying several short Metropolis-type walks, starting from landmark nodes distributed using the scheme of Broder et al. (1994) on a modified input graph. In particular, we obtain an algorithm running in time $tilde O(n+m)$ which is, in general, more space-efficient than both BFS and DFS. We close the paper by showing how to fine-tune the Metropolis-type walk so as to match the performance parameters (e.g., average hitting time) of the unbiased random walk for any graph, while preserving a worst-case bound of $tilde O(n^2)$ on cover time." @default.
- W1585144678 created "2016-06-24" @default.
- W1585144678 creator A5075900164 @default.
- W1585144678 date "2012-04-05" @default.
- W1585144678 modified "2023-09-27" @default.
- W1585144678 title "Faster Walks in Graphs: A $tilde O(n^2)$ Time-Space Trade-off for Undirected s-t Connectivity" @default.
- W1585144678 hasPublicationYear "2012" @default.
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