A Spectrum of Time–Space Trade-offs for Undirecteds-tConnectivity

Uriel Feige
1997 Journal of computer and system sciences (Print)  
We present a family of randomized algorithms that enjoys a wide range of time space trade-offs in deciding undirected S-T-connectivity. Our trade-offs cover the whole range between breadth first search and the random walk procedure of Aleliunas et al., and achieve a time-space product of O (mn) (where n is the number of vertices in the graph, m is the number of edges, and O notation is used in order to suppress logarithmic terms). Moreover, we obtain improved time space trade-offs of O (n 2 )
more » ... r regular graphs. A convenient and informative way of expressing our trade-offs, that implies the trade-offs stated above, is as O where d i is the degree of vertex i in the input graph. In constructing our algorithms and analysing them, we build upon earlier work of Broder et al. (who achieved a time space trade-off of O (m 2 )), Barnes and Feige (who achieved a time space trade-off of O (m 3Â2 n 1Â2 )), and Aldous. In passing, we also improve previous results regarding the rate at which a random walk discovers new vertices in a graph. ] 1997 Academic Press Input to the algorithm. A graph G with n vertices and m edges, two distinguished vertices, S and T. In addition, a parameter p is specified, 1 p n, indicating that the algorithm can use O( p log n) space. Properties of the algorithm. Decides whether S and T are in the same connected component. The algorithm is article no. SS971471 305 0022-0000Â97 25.00
doi:10.1006/jcss.1997.1471 fatcat:uf5k7ro7rzg7lfmuz4qhhushje