N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O((log n)) space. In Proceedings of the 33th IEEE Symposium on Foundations of Computer Science, pages 24--29. Institute of Electrical and Electronics Engineers, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for universal traversal sequences for undirected graphs. Saks and Zhou [SZ99] show that every probabilistic logarithmic space algorithm can be simulated in O(log n) deterministic space. Armoni, Ta Shma, Wigderson and Zhou [ATWZ97] building on work of Nisan, Szemer edi, and Wigderson [NSW92] show that one can solve undirected graph connectivity in O(log 4=3 n) space. 7 Descriptive Complexity Many of the fundamental concepts and methods of complexity theory have their genesis in mathematical logic, and in computability theory in particular. This includes the ideas of reductions, ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 space. In Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science, pages 24-29. IEEE, New York, 1992.

.... SPACE(s) DSPACE(s) The best result known for deterministic simulations of halting bounded error computations with no nontrivial restriction on the number of random bits was proved by Saks and Zhou: This result generalized the previous result of Nisan, Szemeredi and Wigderson [34] that USTCON could be solved in DSPACE( logn) The central ingredient in the deterministic simulations that achieve Theorems 3.4, 3.5 and 3.6 are pseudorandom generators for space bounded computation. The discussion of such generators and their use in these results is the subject of the next ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in o(log 1.5 n) space. In 30th IEEE Symposium on Foundations of Computer Science, pages 24--29, 1992.

.... [2] More recent work presents uniform deterministic polynomial time algorithms for the undirected case using sublinear space (Barnes and Ruzzo [8] and even O(log n) space (Nisan [28] as well as a deterministic algorithm using O(log n) space, but more than polynomial time (Nisan et al. [29]) In this paper we concentrate on the undirected case. The simultaneous time and space requirements of the best known algorithms for undirected graph traversal are as follows. Depth first or breadth first search can traverse any n vertex, m edge undirected graph in O(m n) time, but ....

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log n) space. In Proceedings 33rd Annual Symposium on Foundations of Computer Science, pages 24--29, Pittsburgh, PA, Oct. 1992. IEEE.

....Centre of the Danish National Research Foundation. time. The containment SL RL is the only non trivial one in the line above and follows directly from the randomized Logspace algorithm for USTCON of [AKL 79] It is also known that SL SC [Nis92] SL L L [KW93] and SL DSPACE(log n) NSW92] After the surprising proofs that NL is closed under complement were found [Imm88, Sze88] Borodin et al. [BCD 89] asked whether the same is true for SL. They could prove only the weaker statement, namely that SL co Gamma RL, and left SL = co Gamma SL as an open problem. In this paper ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log n) space. In Proc. 33th IEEE Symposium on Foundations of Computer Science (FOCS), pages 24--29, 1992.

....connectivity problem, Nisan [Nis90] designed a pseudorandom generator that could fool space bounded statistical tests. Building on this idea, Nisan [Nis92] showed how to solve undirected graph connectivity in simultaneous polynomial time and polylogarithmic space. Nisan, Szemer edi, and Wigderson [NSW92] showed how to solve this problem using only O(log 3=2 n) space. Saks and Zhou [SZ95] showed how to simulate BPL in O(log 3=2 n) space, and Armoni, Ta Shma, Wigderson, and Zhou [ATSW 97] showed how to solve undirected graph connectivity in O(log 4=3 n) space. The pseudorandom generator ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proc. 33rd Annual IEEE Symposium on Foundations of Computer Science, pages 24--29, 1992.

....known to have randomized algorithms, their corresponding computations are of, or can be converted to, this type. For space bounded randomized computation, on the other hand, the main approach to derandomization which has been proven effective is the application of pseudorandom generators (see e.g. [Nis92, NSW92, NZ93, SZ95]) 4 1.2 Explicit Constructions Explicit constructions are also called efficient constructions. Generally, the success of reducing randomness by way of constructing combinatorial objects does not merely depend on the existence of the objects, but mainly depends on the efficiency of the ....

....space O(S 2 ) simulations which, for one sided error algorithms, follows from Savitch s Theorem [Sav70] and for two sided error algorithms follows by reduction to recursive matrix exponentiation. Our result includes as a special case the result due to Nisan, Szemer edi and Wigderson [NSW92] that undirected graph connectivity can be computed in space O(log 3=2 n) In Chapter 3 we examine the connection between deterministic amplification and the disperser construction. One problem that is closely related to deterministic amplification is to design randomized algorithms that are ....

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N. Nisan, E. Szemer'edi and A. Wigderson. Undirected Connectivity in O(log 1:5 n) Space. In Proc. of 30th Symposium on Foundations of Computer Science, pp. 248-253, 1992.

....the task of finding for each vertex v of the graph a large virtual neighbourhood. Karger, Nisan and Parnas [KNP92] construct the virtual neighbourhoods using relatively short random walks. A similar approach was used by Aleliunas et al. AKL 79] and recently by Nisan, Szemeredi and Wigderson [NSW92] and Barnes and Feige [BF93] to obtain space efficient algorithms and time space tradeoffs for undirected s t connectivity. Barnes and Feige [BF93] proving a conjecture of Linial, showed that a random walk of length s in an undirected connected graph is likely to visit at least Omega Gamma s ....

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science, Pittsburgh, Pennsylvania, pages 24--29, 1992.

....space. Nisan s result was a breakthrough, since it showed that ustcon algorithms with small space bounds can perform asymptotically better than Savitch s algorithm. Unfortunately, the running time is something like n 45 , 7 making the algorithm extremely impractical. More recently, Nisan et al. NSW92] show the first deterministic algorithm for ustcon with a space bound below Savitch s algorithm. Their algorithm uses pseudorandom generators and a contraction technique similar to that of the algorithms in Chapter 2 to solve undirected connectivity in space O(log 1:5 n) For a further ....

.... the deterministic complexity of ustcon since the results of Chapter 2 were first published [BR91] First, Nisan [Nis92] showed that ustcon was in simultaneous 58 polynomial time and O(log 2 n) space by improving his earlier pseudorandom generator algorithm [Nis90] More recently, Nisan et al. NSW92] show how to solve ustcon in space O(log 1:5 n) and time O(n p log n ) The basic idea of this last result is similar to the recursive algorithm of Section 2.3 the graph is repeatedly contracted by associating a set of vertices with one vertex. The set of vertices is found using the ....

[Article contains additional citation context not shown here]

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, PA, October 1992. IEEE.

.... for undirected connectivity [4, 8] derandomization [1] recycling of random bits [10, 15] approximation algorithms [6, 12, 17] efficient constructions in cryptography [14] and self stabilizing distributed computing [11, 16] Frequently (see, for example, Karger et al. 19] and Nisan et al. [20]) we are interested in E[T (N ) the expected time before a simple random walk on an undirected connected graph, G, visits its N th distinct vertex, N n. The corresponding question for edges is also interesting, and arises in the work of Broder et al. 8] how large is E[T (M) the expected ....

.... results are already known about the properties of short random walks on the special class of graphs known as expanders (see, for example, Ajtai et al. 1] and Jerrum and Sinclair [17] One might hope our results would dramatically improve the algorithms of Karger et al. 19] and Nisan et al. [20] for undirected connectivity. As mentioned above, both require an estimate of E[T (N ) and both used the estimate E[T (N ) O(N 4 ) Unfortunately, substituting our bound only improves the constants for the algorithms, since the running times of both depend on the logarithm of E[T (N ) ....

N. Nisan, E. Szemer' edi, and A. Wigderson, Undirected connectivity in O(log 1:5 n) space, in Proceedings 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, PA, Oct. 1992, IEEE, pp. 24--29.

....reach unambiguity and symmetry. Both RUSPACE(logn) and the symmetric logspace class SymSPACE(logn) possess complete problems and share nearly the same structural upper bounds, 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 ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proc. of 33th Annual IEEE Symposium on Foundations of Computer Science, pages 24--29, 1992.

....1994) It should also be mentioned that the random walk algorithm is far from the only method of deciding reachability in graphs. Reachability questions for arbitrary graphs can be decided in space O(log 2 n) by Savitch s algorithm (1970) and for undirected graphs in space O(log 1:5 n) (Nisan, Szemer edi, Widgerson 1992). Search algorithms such as BFS and IDA have lower time complexities, but require more space. Conclusions and Questions for Further Research The preliminary experiments we have reported indicate that the random walk algorithm may, in cases where it is applicable, be an efficient alternative to ....

Nisan, N.; Szemer'edi, E.; and Widgerson, A. 1992. Undirected connectivity in o(log 1:5 n) space. In Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science, 24 -- 29.

....the same time and space performance. Recent progress has been made on the time space complexity of ustcon. Barnes and Ruzzo [1] show the first sublinear space, polynomial time algorithms for undirected connectivity. Nisan [5] shows that O(log 2 n) space and polynomial time suffice. Nisan et al. [6] show the first ustcon algorithm that uses less space than Savitch s algorithm (O(log 1:5 n) vs. Theta(log 2 n) Prior to the present paper, there was no corresponding sublinear space, polynomial time algorithm known for stcon, and there was some evidence 2 suggesting that none was ....

....Any improvement to the short paths algorithm would probably be very useful in designing future small space stcon algorithms. Our algorithm for stcon does not perform nearly as well as the recent sublinear space algorithms for ustcon by Barnes and Ruzzo [1] Nisan [5] and Nisan et al. [6]. This may be due to a fundamental difference between connectivity on directed and undirected graphs. The results of Barnes and Ruzzo, and of Nisan et al. exploit the symmetry of undirected graphs to group many vertices into one vertex that has the same connectivity properties. Nisan and Nisan et ....

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, PA, Oct. 1992. IEEE.

....conjectured that SL = L. This conjecture is based on the following considerations: The standard complete problem for SL is the graph accessibility problem for undirected graphs (UGAP) Upper bounds on the space complexity of UGAP have been dropping, from log 2 n [26] through log 1. 5 n [19], to log 4 3 n [3] It is suspected that this trend will continue to eventually reach log n. UGAP can be solved in randomized logspace [1] Recent developments in derandomization techniques have led many researchers to conjecture that randomized logspace is equal to L [25] In the context ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log

....wdq above the linear height of the recursion is more than our scheme allows for being log graded. Our scheme captures a stronger self reducibility feature of this problem, one reflected also in the last motivating example. Example 1.3. Undirected s t connectivity: Nisan, Szemer edi, and Wigderson [NSW92] show that the undirected s t connectivity problem has log space instance contraction from n to 2 p log n , and this is the basis of their (log n) 3=2 space algorithm for it. This becomes stepdown r to p r in our framework. Studying problems that admit this kind of instance contraction ....

....and x 2 A ( f(x) 2 A f(x) 1. We call this class simply CFR(log) If f is computable by a finite automaton, we call it CFA. The s t connectivity example in Section 1 belongs to CFR(log) and undirected s t connectivity admits a stronger length contraction from n to 2 p log n in logspace [NSW92]. The second author once hoped that CFR(log) would have some canonical association to NL, but it turns out to be many one equivalent to log space self reducibility as follows. Proposition 4.1 For all types X of Turing, tt , btt , ctt , dtt , or many one query machines, every logspace ....

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proc. 33rd Annual IEEE Symposium on Foundations of Computer Science, pages 24--29, 1992.

.... More recent work presents uniform deterministic polynomial time algorithms for the undirected case using sublinear space (Barnes and Ruzzo [8] and even O(log 2 n) space (Nisan [41] as well as a deterministic algorithm using O(log 1:5 n) space, but more than polynomial time (Nisan et al. [42]) In this paper we concentrate on the undirected case. The simultaneous time and space requirements of the best known algorithms for undirected graph traversal are as follows. Depth first or breadth first search can traverse any n vertex, m edge undirected graph in O(m n) time, but requires ....

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proceedings 33rd Annual Symposium on Foundations of Computer Science, pages 24--29, Pittsburgh, PA, Oct. 1992. IEEE.

....tools to derive efficient deterministic algorithms from their randomized counterparts, has blossomed greatly in the last decade. The best known deterministic solutions for several classical problems such as testing undirected graph connectivity within limited space bounds, take this approach [24]. Two motivations for research in this area are the nonavailability of perfect random sources, and the need for absolute (non probabilistic) guarantees of correctness in, say, critical applications. The fact that computers do not use real random sources prevents randomized algorithms from ....

N. Nisan, E. Szemer'edi, and A. Wigderson, Undirected connectivity in O(log 1:5 n) space, in Proc. IEEE Symposium on Foundations of Computer Science, pages 24--29, 1992.

....the same time and space performance. Recent progress has been made on the time space complexity of ustcon. Barnes and Ruzzo [1] show the first sublinear space, polynomial time algorithms for undirected connectivity. Nisan [5] shows that O(log 2 n) space and polynomial time suffice. Nisan et al. [6] show the first ustcon algorithm that uses less space than Savitch s algorithm (O(log 1:5 n) vs. 2(log 2 n) Prior to the present paper, there was no corresponding sublinear space, polynomial time algorithm known for stcon, and there was some evidence suggesting that none was possible. It ....

....= dlog ne. Any improvement to the short paths algorithm would probably be very useful in designing future small space stcon algorithms. Our algorithm for stcon does not perform nearly as well as the recent sublinear space algorithms for ustcon by Barnes and Ruzzo [1] Nisan [5] and Nisan et al. [6]. This may be due to a fundamental difference between connectivity on directed and undirected graphs. The results of both Barnes and Ruzzo, and of Nisan et al. exploit the symmetry of undirected graphs to group many vertices into one vertex that has the same connectivity properties. Nisan and ....

N. Nisan, E. Szemeredi, and A. Widgerson. Undirected connectivity in O(log 1:5 n) space. Manuscript, Dec. 1991.

....simulate Nisan s algorithm on the UGAP instance; each time this algorithm tries to read from the input matrix, we first solve the SC 2 problem encountered in the corresponding entry of the input. In a simular way, it is possible to show that the containment of SL in DSPACE(log 1:5 n) see [NSW92] yields: Corollary 5.19 RN (O(1) poly(N) DSPACE(log 1:5 n) In the second half of this subsection we will prove the converse of Theorem 5.17. Theorem 5.20 SLH RN (O(1) poly(N) The proof will be done by proving O Sigma SL k RN (O(1) poly(N) via induction over k. To show the case k ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proc. of 34th Annual IEEE Symposium on Foundations of Computer Science, 1992.

No context found.

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O((log n)) space. In Proceedings of the 33th IEEE Symposium on Foundations of Computer Science, pages 24--29. Institute of Electrical and Electronics Engineers, 1992.

No context found.

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In 33rd FOCS, pages 24-29, 1992.

....Logspace machine running in polynomial time. The containment SL RL is the only non trivial one in the line above and follows directly from the randomized Logspace algorithm for USTCON of [AKL 79] It is also known that SL SC [Nis92] SL L L [KW93] and SL DSPACE(log 1:5 n) NSW92] After the surprising proofs that NL is closed under complement were found [Imm88, Sze88] Borodin et al. [BCD 89] asked whether the same is true for SL. They could prove only the weaker statement, namely that SL coRL, and left SL = coSL as an open problem. In this paper we solve the ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proc. 33th IEEE Symposium on Foundations of Computer Science (FOCS), pages 24--29, 1992.

....Logspace machine running in polynomial time. The containment SL RL is the only non trivial one in the line above and follows directly from the randomized Logspace algorithm for USTCON of [AKL 79] It is also known that SL SC [Nis92] SL L L [KW93] and SL DSPACE(log 1:5 n) NSW92] After the surprising proofs that NL is closed under complement were 1 4 found [Imm88, Sze88] Borodin et al. BCD 89] asked whether the same is true for SL. They could prove only the weaker statement, namely that SL coRL, and left iSL = coSL j as an open problem. In this paper we solve ....

N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O((log 1:5 n)) space. In Proceedings of the 33th IEEE Symposium on Foundations of Computer Science, pages 2429. Institute of Electrical and Electronics Engineers, 1992.

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N. Nisan, E. Szemeredi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proceedings of the 30th FOCS, pages 24-29, 1989.

No context found.

N. Nisan, E. Szemer'edi, and A. Wigderson. Undirected connectivity in O(log 1:5 n) space. In Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science, Pittsburgh, Pennsylvania, pages 24--29, 1992.

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N Nisan, E Szemeredi, and A Wigderson. Undirected connectivity in O(log n) space. In Proceedings of the 33rd Annual Smposium on Foundations of Computer Science, pages 24--29. IEEE Computer Society Press, 1992.

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