Simulating undirected st-connectivity algorithms on uniform JAGs and NNJAGs

  • Authors:

  • Pinyan Lu;Jialin Zhang;Chung Keung Poon;Jin-Yi Cai

  • Affiliations:

  • State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China;Department of Physics, Tsinghua University, Beijing, China;Department of Computer Science, City University of Hong Kong, Hong Kong, China;,Computer Sciences Department, University of Wisconsin, Madison, WI

  • Venue:
  • ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
  • Year:
  • 2005

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Abstract

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 of $\mathcal{RL}$ or $\mathcal{NL}$. In this paper, we show that Reingold's algorithm, the O(log4/3n)-space algorithm by Armoni et al.[3] and the O(log3/2n)-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(log2n) 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.