Omer Reingold, Luca Trevisan, Salil Vadhan

Motivated by Reingold's recent deterministic log-space algorithm for Undirected S-T Connectivity (ECCC TR 04-94), we revisit the general RL vs. L question, obtaining the following results.

1. We exhibit a new complete problem for RL: S-T Connectivity restricted to directed graphs for which the random walk is promised to have ... more >>>

Eyal Rozenman, Salil Vadhan

We introduce a "derandomized" analogue of graph squaring. This

operation increases the connectivity of the graph (as measured by the

second eigenvalue) almost as well as squaring the graph does, yet only

increases the degree of the graph by a constant factor, instead of

squaring the degree.

One application of ... more >>>