G. Barnes, J. Buss, W. Ruzzo, and B. Schieber. A sub-linear space, polynomial time algorithm for directed s-t connectivity. In 7th annual conference on Structure in Complexity Theory, pages 27-33, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....2 n) time. Nevertheless, these two results imply that stcon is in P Polylogspace. Tompa [Tom82] shows that a certain natural approach, repeated squaring, for computing stcon has no implementation which runs in polynomial time and sub linear space simultaneously. However, Barnes et al. BBRS92] construct an algorithm which uses only n=2 Omega Gamma p log n) space (which is sub linear) while keeping polynomial running time. This shows that the repeated squaring method is too restricted. Futhermore, their algorithm implies a general time space tradeoff of T = 2 O(log 2 (n log ....

....probabilistic NNJAG which gives a super polynomial lower bound on time when S is sufficiently small. For example, when S is at most n ffl for any constant 0 ffl 1, T is at least 2 Omega Gamma log 2 n log log n ) This lower bound also closely matches the upper bound of Barnes et al. BBRS92] which can be implemented on an NNJAG as implied by Chapter 4. The result presented in Chapter 5 is joint work with Edmonds. Finally, in Chapter 6, some future directions for answering questions (Q1 0 ) and 6 (Q2 0 ) are discussed. 7 Chapter 2 Models of Computation In this chapter, we ....

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Greg Barnes, Jonathan F. Buss, Walter L. Ruzzo, and Baruch Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, Structure in Complexity Theory, Seventh Annual Conference, pages 27--33, Boston, MA, June 1992. IEEE.

....In this section we give lower bounds of 2 #(d) m, resp. d #(log d) m for a locally greedy, a generalized greedy, a depth first, and a breadth first algorithm. A related problem for which lower bounds have been studied extensively, is the s t connectivity problem in directed graphs, see [3, 4, 14] and references therein. Given a directed graph, the problem is to decide whether there exists a path from a distinguished node s to a distinguished node t . Most of the results are developed 3 in the JAG model by Cook and Rackoff [10] The best time space tradeoffs currently known [4, 14] only ....

G. Barnes, J.F. Buss, W.L. Ruzzo and B. Schieber. A sublinear space, polynomial time algorithms for directed s--t connectivity. Proc. 7th Annual Conf. on Structure in Compexity Theory, 27--33, 1992.

....d) m for a locally greedy, a depth first and a breadth first algorithm. We also give a lower bound of d Omega Gamma194 d) m for a generalized greedy strategy. A related problem for which lower bounds have been studied extensively, is the s t connectivity problem in directed graphs, see [3, 4, 14] and references therein. Given a directed graph, the problem is to decide whether there exists a path from a distinguished node s to a distinguished node t. Most of the results are developed in the JAG model by Cook and Rackoff [10] The best time space tradeoffs currently known [4, 14] only ....

G. Barnes, J.F. Buss, W.L. Ruzzo and B. Schieber, A sublinear space, polynomial time algorithms for directed s--t connectivity, in Proc. 7th Annual Conf. on Structure in Compexity Theory, 1992, pp. 27--33.

....on each node when it first visits it. This uses O (n log n) space. Cook and Rackoff [CR80] show that the JAG model is powerful enough to execute an adaptation of Savitch s algorithm [Sa70] for directed st connectivity using only O i log 2 n j space. Poon [Po93a] shows that Barnes et al. [BBRS92] sub linear space, polynomial time algorithm for directed s t connectivity runs on a JAG as well. Furthermore, Savitch [Sa73] shows that if one allows the JAG the additional ability to move pebbles from each node i to node i 1, for an arbitrary ordering of the nodes) then the model can simulate ....

G. Barnes, J. Buss, W. Ruzzo, and B .Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings of the Seventh Annual Conference, Structure in Complexity Theory, pages 27--33, Boston, MA, June 1992.

.... lower bound of ST 2 Omega Gamma n 2 = log n) on the JAG model by Barnes and Edmonds [BE93] and that of S 1=3 T 2 Omega Gamma n 4=3 ) on the NNJAG model by Edmonds [Edm93a] Our lower bound is tight for S 2 O(n 1 Gammaffi ) for any ffi 0, matching the upper bound of Barnes et al. BBRS92] As a corollary of this improved lower bound we obtain the first tight space lower bound of Omega Gamma 24 2 n) on the NNJAG model. No tight space lower bound was previously known even for the more restricted JAG model. 1 Introduction The st connectivity problem (stcon) is a fundamental ....

....[Sav70] provided an algorithm that uses O(log 2 n) space and requires time exponential in its space bound (i.e. time n O(logn) Tompa [Tom82] showed that stcon cannot be solved in polynomial time and sublinear space simultaneously by the repeated squaring method. However, Barnes et al. BBRS92] gave a polynomial time algorithm for stcon that uses space S 2 n=2 Theta( p log n) providing the first polynomial time, sub linear space algorithm. This shows that the repeated squaring method is too restricted. In fact, their algorithm implies a general time space upper bound of T 2 2 ....

[Article contains additional citation context not shown here]

Greg Barnes, Jonathan F. Buss, Walter L. Ruzzo, and Baruch Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, Structure in Complexity Theory, Seventh Annual Conference, pages 27--33, Boston, MA, June 1992. IEEE.

....more time when the space allocated to the model is bounded. Savitch s algorithm [Sa70] uses only O i log 2 n j space, but requires 2 O(log 2 n) time. It is only recently that a polynomial time, sub linear O i n 2 p log n j space algorithm was found for directed st connectivity [BBRS92]. Section 1.1 stated that the JAG model is general enough so that most known algorithms for graph connectivity can be implemented on it. I will now be more specific. It can perform depth first or breadth first search. It avoids cycling by leaving a pebble on each node when it first visits it. This ....

....log n Delta time using a universal traversal sequence [CRRST89, KLNS89] For directed graphs, Cook and Rackoff [CR80] show that the JAG model is powerful enough to execute an adaptation of Savitch s algorithm [Sa70] which uses O i log 2 n j space. Poon [Po93a] shows that Barnes et al. s [BBRS92] sub linear space, polynomial time algorithm for directed st connectivity runs on a JAG as well. 1.4 A History of Lower Bounds for st Connectivity A number of space lower bounds have been obtained (even when an unbounded amount of time is allowed) Cook and Rackoff [CR80] prove a lower bound ....

G. Barnes, J. Buss, W. Ruzzo, and B .Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings of the Seventh Annual Conference, Structure in Complexity Theory, pages 27--33, Boston, MA, June 1992.

No context found.

G. Barnes, J. Buss, W. Ruzzo, and B. Schieber. A sub-linear space, polynomial time algorithm for directed s-t connectivity. In 7th annual conference on Structure in Complexity Theory, pages 27-33, 1992.

....can be traversed nondeterministically in polynomial time and logarithmic space simultaneously, it is not widely believed that they can be traversed deterministically in polynomial time and small space simultaneously. See Tompa [32] and Edmonds and Poon [22] for lower bounds, and Barnes et al. [5] for an upper bound. In contrast, undirected graphs can be traversed in polynomial time and logarithmic space probabilistically by using a random walk (Aleliunas et al. 2] Borodin et al. 15] this implies similar resource bounds on (nonuniform) deterministic algorithms (Aleliunas et al. 2] ....

G. Barnes, J. F. Buss, W. L. Ruzzo, and B. Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, Structure in Complexity Theory, Seventh Annual Conference, pages 27--33, Boston, MA, June 1992. IEEE. To appear, SIAM Journal on Computing.

....that appear in Chapter 2. Most of this chapter appeared in the 1991 ACM Symposium on Theory of Computing [BR91] Later, with the help of Jonathan Buss and Baruch Schieber, Larry and I came up with the remainder of Chapter 3, which appeared in the 1992 Structure in Complexity Theory Conference [BBRS92] Throughout my graduate student career, Larry has been a good advisor, a good listener, and a good friend. Without his direction and assistance, this thesis would not have been written. I am also indebted to Paul Beame and Martin Tompa, the other two members of my reading committee, who ....

G. Barnes, J. F. Buss, W. L. Ruzzo, and B. Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, 72 Structure in Complexity Theory, Seventh Annual Conference, Boston, MA, June 1992. IEEE. To appear.

....can be traversed nondeterministically in polynomial time and logarithmic space simultaneously, it is not widely believed that they can be traversed deterministically in polynomial time and small space simultaneously. See Tompa [48] and Edmonds and Poon [27] for lower bounds, and Barnes et al. [5] for an upper bound. In contrast, undirected graphs can be traversed in polynomial time and logarithmic space probabilistically by using a random walk (Aleliunas et al. 2] Borodin et al. 17] this implies similar resource bounds on (nonuniform) deterministic algorithms (Aleliunas et al. 2] ....

G. Barnes, J. F. Buss, W. L. Ruzzo, and B. Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, Structure in Complexity Theory, Seventh Annual Conference, pages 27--33, Boston, MA, June 1992. IEEE. To appear, SIAM Journal on Computing.

....breadth and depth first search, run in optimal time Theta(m n) and use Theta(n log n) space. At the other extreme, Savitch s Theorem [15] provides a small space ( Theta(log 2 n) algorithm that requires time exponential in its space bound (i.e. time n Theta(log n) Barnes et al. [1] show the first sublinear space, polynomial time algorithm for stcon. All of these algorithms can be implemented on the standard JAG [8, 14] Using the NNJAG s ability to access the names of the nodes in the graph, Poon [13] shows how to implement Immerman s and Szelepcs enyi s nondeterministic ....

G. Barnes, J. F. Buss, W. L. Ruzzo, and B. Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, Structure in Complexity Theory, Seventh Annual Conference, pages 27--33, Boston, MA, June 1992. IEEE. Submitted for publication.

....although directed graphs can be traversed nondeterministically in polynomial time and logarithmic space simultaneously, it is not widely believed that they can be traversed deterministically in polynomial time and small space simultaneously. See Tompa [35] for a lower bound, and Barnes et al. [5] for an upper bound. In contrast, undirected graphs can be traversed in polynomial time and logarithmic space probabilistically by using a random walk (Aleliunas et al. 2] Borodin et al. 13] this implies similar resource bounds on (nonuniform) deterministic algorithms (Aleliunas et al. 2] ....

G. Barnes, J. F. Buss, W. L. Ruzzo, and B. Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Proceedings, Structure in Complexity Theory, Seventh Annual Conference, pages 27--33, Boston, MA, June 1992. IEEE.

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