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Conference Papers Year : 2013

A $\tilde O(n^2)$ Time-Space Trade-off for Undirected s-t Connectivity


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 $S\cdot T = \tilde O(n^2)$ 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.
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Dates and versions

hal-00685373 , version 1 (05-04-2012)
hal-00685373 , version 2 (13-04-2012)
hal-00685373 , version 3 (10-07-2012)



Adrian Kosowski. A $\tilde O(n^2)$ Time-Space Trade-off for Undirected s-t Connectivity. SODA - 24th ACM-SIAM Symposium on Discrete Algorithms, Jan 2013, New Orleans, United States. pp.1873-1883. ⟨hal-00685373v3⟩
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