A sublinear space, polynomial time algorithm for directed s-t connectivity

A deterministic sublinear space, polynomial-time algorithm for directed s-t connectivity, which is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph, is presented. For n-vertex graphs, the algorithm can use as little as n/2/sup Theta /( square root log n) space while still running in polynomial time.<<ETX>>

[1]  Christos H. Papadimitriou,et al.  Symmetric Space-Bounded Computation , 1982, Theor. Comput. Sci..

[2]  Noam Nisan,et al.  RL⊆SC , 1992, STOC '92.

[3]  Kurt Mehlhorn,et al.  The Recognition of Deterministic CFL's in Small Time and Space , 1983, Inf. Control..

[4]  Stephen A. Cook,et al.  Space Lower Bounds for Maze Threadability on Restricted Machines , 1980, SIAM J. Comput..

[5]  Walter L. Ruzzo,et al.  Deterministic algorithms for undirected s-t connectivity using polynomial time and sublinear space. , 1991, STOC '91.

[6]  Chung Keung Poon.  Space bounds for graph connectivity problems on node-named JAGs and node-ordered JAGs , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[7]  Avi Wigderson,et al.  Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing , 1992, Symposium on the Theory of Computing.

[8]  Endre Szemerédi,et al.  Undirected Connectivity in O(log ^1.5 n) Space , 1992, FOCS.

[9]  E. Szemerédi,et al.  Undirected connectivity in O(log/sup 1.5/n) space , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[10]  Avi Wigderson,et al.  The Complexity of Graph Connectivity , 1992, MFCS.

[11]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[12]  J. Edmonds,et al.  Time-space lower bounds for directed s-t connectivity on JAG models , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[13]  Stephen A. Cook,et al.  Deterministic CFL's are accepted simultaneously in polynomial time and log squared space , 1979, STOC.

[14]  Martin Tompa,et al.  Two familiar transitive closure algorithms which admit no polynomial time, sublinear space implementations , 1980, STOC '80.