An O(log(n)4/3) space algorithm for (s, t) connectivity in undirected graphs

We present a deterministic algorithm that computes <italic>st</italic>-connectivity in undirected graphs using <italic>O</italic>(log <supscrpt>4/3</supscrpt><italic>n</italic>) space. This improves the previous <italic>O</italic>(log<supscrpt>3/2</supscrpt><italic>n</italic>) bound of Nisan et al. [1992].

[1]  BPHSPACE ( S ) DSPACE ( S 3 2 ) * , 1999 .

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

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

[4]  Uriel Feige,et al.  Short random walks on graphs , 1993, SIAM J. Discret. Math..

[5]  Endre Szemerédi,et al.  Undirected Connectivity in O(l~gl*~ n) Space* , 1992 .

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

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

[8]  Mihir Bellare,et al.  Randomness-efficient oblivious sampling , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[9]  Richard J. Lipton,et al.  Random walks, universal traversal sequences, and the complexity of maze problems , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[10]  David Zuckerman,et al.  Randomness-optimal sampling, extractors, and constructive leader election , 1996, STOC '96.

[11]  Noam Nisan,et al.  Pseudorandom generators for space-bounded computation , 1992, Comb..

[12]  Noam Nisan Rl <= Sc , 1994, Comput. Complex..

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