R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovasz, and C. Racko#. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science. Institute of Electrical and Electronics Engineers, 1979. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Randomization and Derandomization in Space-Bounded Computation - Saks (1996) (14 citations) (Correct)
....In this section, we review in detail the results summarized in figure 3. At the same time, we highlight various questions that point in the direction of figure 4. 3. 1 Solving USTCON in RHL The most well known use of probabilism in spacebounded computation is the result of Aleliunas et al. [3] showing how USTCON can be decided in RHL. By our earlier remark that SSPACE(s) can be reduced to a USTCON problem on a graph of size 2 this implies that SSPACE(s) RHSPACE(s) Given the n vertex graph G and vertices s and t, the randomized algorithm for USTCON is to start at vertex s and ....
R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, and C. Racko#. Random walks, universal sequences and the complexity of maze problems. In 20th IEEE Symposium on Foundations of Computer Science, pages 218--223, 1979.
Space Efficient Algorithms for Series-Parallel Graphs - Jakoby, Liskiewicz, Reischuk (2001) (Correct)
....undirected case series parallel graphs can be characterized as the set of graphs containing no clique of size 4 as a minor [10] In contrast to the series parallel graph family, the reachability problem for arbitrary graphs seems to be easier in the undirected case than in the directed case. From [1] we know that the undirected version can be solved by a randomized log space bounded machine, whereas no randomized algorithm is known for the directed case. Are there other distinctions of this kind Acknowledgment: Thanks are due to Eric Allender and Markus Blaser for helpful comments and ....
R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, C. Rackoff, Random Walks, Universal Sequences and the Complexity of Maze Problems, Proc. 20. FOCS, 1979, 218-223.
Space Efficient Algorithms for Series-Parallel Graphs - Jakoby, Liskiewicz, Reischuk (2000) (Correct)
....undirected graph corresponding to b) Note that c) is series parallel, while d) is a 4 clique and thus not series parallel. 11 In contrast to the series parallel graph family, the reachability problem for arbitrary graphs seems to be easier in the undirected case than in the directed case. From [1] we know that the undirected version can be solved by a randomized log space bounded machine, whereas no randomized algorithm is known for the directed case. Are there other distinctions of this kind Acknowledgment: Thanks are due to Eric Allender and Markus Blaser for helpful comments and ....
R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, C. Rackoff, Random Walks, Universal Sequences and the Complexity of Maze Problems, Proc. 20. FOCS, 1979, 218-223.
Reducing Randomness In Computation Via Explicit Constructions - Zhou (1996) (Correct)
....understand how much power randomness can provide over determinism. For many problems, a randomized algorithm is by far faster (e.g. primality testing [SS77, Rab80, AH87] more parallel (e.g. perfect matching construction [KUW86, MVV87] more space efficient (e.g. undirected graph connectivity [AKLLR79]) or simpler (e.g. the min cut problem [Kar93] than any known deterministic algorithm. In fact, there are many problems such as primality testing, perfect matching construction and undirected graph connectivity which (in certain respects) have very efficient randomized algorithms, but are not ....
....[Nis90] which he used to show that RL (i.e. RHSPACE(logn) can be simulated by a deterministic algorithm that is simultaneously in polynomial time and O(log 2 n) space. Using Nisan s generator, Nisan, Szemer edi, Wigderson [NSW92] showed that undirected (s; t) connectivity, which is in RL [AKLLR79] and is complete for the complexity class SL [LP82] can be computed in DSPACE(log 3=2 n) It was this result that motivated our research that we present in this work. As with these other results, Nisan s pseudorandom generator is a major component of our simulation. One key observation that ....
R. Aleliunas, R. Karp, R. Lipton, L. Lovasz and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proc. of 20th IEEE Symposium on Foundations of Computer Science, pp. 218223, 1979.
An Unambiguous Class Possessing a Complete Set - Lange (1996) (4 citations) (Correct)
.... which seem to distinguish them from NSPACE(logn) they are contained in parity logspace, DSPACE(o(log 2 n) and SC 2 ( 12,16,4,17,2] Open questions here are: what is the relationship between SymSPACE(logn) and RUSPACE(logn) Can the inclusion of SymSPACE(logn) in randomized logspace ([1]) be extended to RUSPACE(logn) If so, the deterministic space bound of O(log 2 n= log log n) for RUSPACE(logn) could be improved to O(log 1:5 n) 18] Can the inclusion RUSPACE(logn) LOG(DCFL) be extended to SymSPACE(log n) If so, the currently best known CREW PRAM running time for ....
R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proc. of 20rd FOCS, pages 218--223, 1979.
RL ⊆ SC - Nisan (1995) (Correct)
....but which requires super polynomial time. It is a long standing open problem whether there exists an algorithm for st connectivity that combines both features: runs in polynomial time and poly logarithmic space. For st connectivity in undirected graphs two more types of algorithms are known. In [AKL 79] a randomized Logspace (and polynomial time) algorithm is given. A zero error version of this type of algorithm is given in [BCD 89] As for deterministic algorithms, Barnes and Ruzzo [BR91] recently presented an algorithm for undirected st connectivity that runs in polynomial time and n ffl ....
....problem that runs in polynomial time and O(log 2 n) space. Unfortunately, the running time of the algorithm is a high order polynomial (something like n 45 ) We do not know how to improve the running time significantly. The algorithm is obtained by derandomizing the randomized algorithm of [AKL 79]. In fact, the derandomization result is very general. We prove that any problem that can be computed in randomized Logspace has a deterministic algorithm that runs in polynomial time and O(log 2 n) space. In terms of complexity classes we can state our result as: Theorem 2: BPL SC: For ....
[Article contains additional citation context not shown here]
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In 20 th Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1979.
Lower Bounds for Deterministic and Nondeterministic Branching.. - Razborov (1991) (50 citations) (Correct)
....out nevertheless that they capture in the same fashion nondeterministic space. That is, NLOGSPACE=poly = RS(poly) How about switching networks It follows from (1) and (3) that LOGSPACE=poly S(poly) On the other hand, UNDIRECTED GRAPH ACCESSIBILITY is doable in random logarithmic space [3] which implies the converse inclusion. Hence LOGSPACE=poly = S(poly) 4) 3) and (4) imply BP (f) S(f) O(1) 5) It is worth noting that no constructive proof of (5) is known. It follows from the discussion above that Boolean simulations (1) actually reflect class inclusions P NLOGSPACE ....
R. Aleluinas, R. M. Karp, R. J. Lipton, R. J. Lov'asz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th IEEE Symposium on Foundations of Computer Science, pages 218--223, 1979.
Symmetric Logspace is Closed under Complement - Nisan, al. (1995) (24 citations) (Correct)
No context found.
R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovasz, and C. Racko#. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science. Institute of Electrical and Electronics Engineers, 1979.
An Optimal Randomized Logarithmic Time Connectivity Algorithm .. - Halperin, Zwick (1994) (12 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Racko . Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 218-223, 1979.
Refining Randomness - Ta-Shma (1996) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science, 1979.
Lower Bounds for Deterministic and Nondeterministic Branching.. - Razborov (1991) (50 citations) (Correct)
No context found.
R. Aleluinas, R. M. Karp, R. J. Lipton, R. J. Lov'asz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th IEEE Symposium on Foundations of Computer Science, pages 218--223, 1979.
Optimal randomized EREW PRAM algorithms for finding spanning.. - Halperin, Zwick (2000) (9 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 218--223, 1979.
Symmetric Logspace is Closed Under Complement - Nissin, al. (1994) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science, 1979.
An Optimal Randomized Logarithmic Time Connectivity Algorithm .. - Halperin, Zwick (1996) (12 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 218--223, 1979.
Refining Randomness - Ta-Shma (1996) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science, 1979.
Symmetric Logspace is Closed Under Complement - Nisan, Ta-Shma (1995) (24 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science, 1979.
Symmetric Logspace is Closed Under Complement - Nisan (1995) (24 citations) (Correct)
No context found.
R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovasz, and C. Rackooe. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science. Institute of Electrical and Electronics Engineers, 1979.
An Optimal Randomized Logarithmic Time Connectivity Algorithm .. - Halperin, Zwick (1994) (12 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 218--223, 1979.
... - Armoni, Ta-Shma, Wigderson, Zhou (1996) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science, 1979.
Optimal randomized EREW PRAM algorithms for finding spanning.. - Halperin, Zwick (1996) (9 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 218--223, 1979.
Symmetric Logspace is Closed Under Complement - Nisan, Ta-Shma (1994) (24 citations) (Correct)
No context found.
R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on the Foundations of Computer Science, 1979.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC