Undirected ST-Connectivity in Log-Space PRELIMINARY VERSION: PLEASE DO NOT DISTRIBUTE
نویسنده
چکیده
We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this algorithm implies that SL = L (where L is the class of problems solvable by deterministic log-space computations). Our algorithm also implies log-space constructible universal-traversal sequences for graphs with restricted labelling and log-space constructible universal-exploration sequences for general graphs.
منابع مشابه
Undirected ST-Connectivity in Log-Space PRELIMINARY VERSION
We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this al...
متن کاملSimulating 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 ...
متن کاملLecture 18 Lecturer
In this lecture we present the relatively recent fundamental result of O. Reingold [3] which establishes that undirected st-connectivity can be decided in deterministic logarithmic space. Given an undirected graph G, two vertices s and t in G, USTCON(G, s, t) is the problem of deciding whether there exists a path in G connecting s and t. The more difficult, directed graph version of this proble...
متن کاملTight Lower Bounds for st-Connectivity on the NNJAG Model
Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218–227]. Let n be the number of nodes in the input graph and S and T...
متن کاملUndirected Connectivity in O(log
We present a deterministic algorithm for the connectivity problem on undirected graphs that runs in O(log n) space. Thus, the recursive doubling technique of Savich which requires Θ(log n) space is not optimal for this problem.
متن کاملAn Interview with Vladimir Trifonov ( 2005
The 2005 Danny Lewin Prize for the best student paper at STOC was awarded to Vladimir Trifonov, of the University of Texas at Austin, for his paper “An O(logn log log n) Space Algorithm for Undirected st-Connectivity” [1]. Hal Gabow recently started the tradition of interviewing the Danny Lewin Prize winner and publishing the interview in SIGACT News. (An interview with the 2003 winner Tom Haye...
متن کامل