Simulating Undirected st-Connectivity Algorithms on Uniform JAGs and NNJAGs

In a breakthrough result, Reingold [17] showed that the Undirected st-Connectivity problem can be solved in O(log n) space. The next major challenge in this direction is whether one can extend it to directed graphs, and thereby lowering the deterministic space complexity ofRL or NL. In this paper, we show that Reingold’s algorithm, the O(log n)space algorithm by Armoni et al. [3] and the O(log n)-space algorithm by Nisan et al. [14] can all be carried out on the RAM-NNJAG model [15] (a uniform version of the NNJAG model [16]). As there is a tight Ω(log n) space lower bound for the Directed st-Connectivity problem on the RAM-NNJAG model implied by [8], our result gives an obstruction to generalizing Reingold’s algorithm to the directed case.