Abstract
We present a spectrum of randomized time-space tradeoffs for solving directed graph connectivity or STCONN in small space. We use a strategy parameterized by a parameter k that uses k pebbles and performs short random walks of length \(n^{\frac{1}{k}}\) using a probabilistic counter. We use this to get a family of algorithms that ranges between log2 n and log n in space and 2\(^{{\rm log^2}n}\) and n n in running time. Our approach allows us to look at Savitch’s algorithm and the random walk algorithm as two extremes of the same basic divide and conquer strategy.
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References
Aleliunas, R., Karp, R., Lipton, R., Lovasz, L., Rakoff, C.: Random walks, universal traversal sequences, and the complexity of maze problems. In: 20th Annual Symposium on Foundations of Computer Science, pp. 218–223 (1979)
Armoni, R., Ta-Shma, A., Wigderson, A., Zhou, S.: An log(n)4/3 space algorithm for s-t connectivity in undirected graphs. Journal of the ACM 47, 294–311 (2000)
Barnes, G., Buss, J., Ruzzo, W., Schieber, B.: A sub-linear space, polynomial time algorithm for directed s-t connectivity. In: 7th annual conference on Structure in Complexity Theory, pp. 27–33 (1992)
Berman, P., Simon, J.: Lower bounds on graph threading by probabilistic machines. In: 24th Annual Symposium on Foundations of Computer Science, pp. 304–311 (1983)
Cook, S., Rackoff, C.: Space lower bounds for maze threadability on restricted machines. SIAM Journal on Computing 9(3), 636–652 (1980)
Edmonds, J., Poon, C., Achlioptas, D.: Tight lower bounds for st-connectivity on the NNJAG model. SIAM J. Comput. 28(6), 2257–2284 (1999)
Feige, U.: A spectrum of time-space tradeoffs for undirected s-t connectivity. Journal of Computer and System Sciences 54(2), 305–316 (1997)
Gill, J.: Computational complexity of probabilistic turing machines. In: Proc. 6th Annual ACM Symp. Theory of Computing, pp. 91–95 (1974)
Nisan, N.: RL ⊂ SC. Journal of Computational Complexity 4, 1–11 (1994)
Nisan, N., Szemeredi, E., Wigderson, A.: Undirected connectivity in O(log1.5n) space. In: Proceedings of the 30th FOCS, pp. 24–29 (1989)
Poon, C.: Personal communication
Poon, C.: Space bounds for graph connectivity problems on node named jags and node ordered jags. In: 34th Annual Symposium on Foundations of Computer Science, pp. 218–227 (1993)
Poon, C.: On the complexity of the s-t connectivity problem. Ph.D Thesis, University of Toronto (1996)
Savitch, W.: Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences 4(2), 177–192 (1970)
Saks, M.: Randomization and derandomization in space-bounded computation. In: Annual Conference on Structure in Complexity Theory (1996)
Simon, J.: Space-bounded probabilistic turing machine complexity classes are closed under complement. In: Proc. 13th Annual ACM Symp. Theory of Computing, pp. 158–167 (1981)
Wigderson, A.: The complexity of graph connectivity. In: Proceedings of the 17th Mathematical Foundations of Computer Science, pp. 112–132 (1992)
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Gopalan, P., Lipton, R.J., Mehta, A. (2003). Randomized Time-Space Tradeoffs for Directed Graph Connectivity. In: Pandya, P.K., Radhakrishnan, J. (eds) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2003. Lecture Notes in Computer Science, vol 2914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24597-1_18
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DOI: https://doi.org/10.1007/978-3-540-24597-1_18
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