A $\tilde O(n^2)$ Time-Space Trade-off for Undirected s-t Connectivity
KOSOWSKI, Adrian
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
KOSOWSKI, Adrian
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
< Reduce
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Language
en
Communication dans un congrès
This item was published in
SODA - 24th ACM-SIAM Symposium on Discrete Algorithms, 2013-01, New Orleans. 2013-01p. 1873-1883
SIAM
English 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 ...Read more >
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.Read less <
English Keywords
undirected s-t connectivity
time-space trade-off
graph exploration
Metropolis-Hastings walk
parallel random walks
Origin
Hal imported