G. Barnes and J. A. Edmonds. Time-space lower bounds for directed s-t connectivity on JAG models. In Proceedings 34th Annual Symposium on Foundations of Computer Science, pages 228--237, Palo Alto, CA, Nov. 1993. IEEE.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....see Sections 3 and 4. We prove upper and lower bounds for undirected graph problems on other variants of the JAG in a companion paper [10] Following the preliminary appearance of these results, Edmonds [21] proved a much stronger result for traversing undirected graphs, and Barnes and Edmonds [6] and Edmonds and Poon [22] proved even more dramatic tradeoffs for traversing directed graphs. 2. Walking Automata for Graphs The problem we will be considering is undirected st connectivity : given an undirected graph G and two distinguished vertices s and t, determine if there is a path from ....

G. Barnes and J. A. Edmonds. Time-space lower bounds for directed s-t connectivity on JAG models. In Proceedings 34th Annual Symposium on Foundations of Computer Science, pages 228--237, Palo Alto, CA, Nov. 1993. IEEE.

.... of a deterministic Turing machine by an alternating machine) and Paul, Pippenger, Szemeredi and Trotter [PPST83] non deterministic linear time is not a subset of deterministic linear time) Time space lower bounds have also been shown for other models such as Jumping Automata for Graphs (JAG) [Edm98, BE98, EP95], branching programs [Kar86, BST98, Bea91] and comparison models [Yao94] 2 Preliminaries We will use the multi tape Turing machine model to prove the main theorem. Let N(t) and D(t) denote the classes of all languages accepted by Turing machines running in nondeterministic time O(t) and ....

Greg Barnes and Jeff A. Edmonds. Time-space lower bounds for directed st-connectivity on graph automata models. SIAM Journal on Computing, 27(4):1190--1202, August 1998.

....extended by Berman and Simon [BS83] to a randomized JAG. More precisely, they show that any randomized JAG solving stcon with at most 2 log c n time requires at least c 0 log 2 n= log log n space where c 0 is a constant depending on c. For the time space tradeoff, Barnes and Edmonds [BE93] prove a lower bound of T = Omega Gamma n 2 = S log n) on the JAG model. On a more general model called the NNJAG 4 model (Node Named JAG) to be defined in the next chapter, Edmonds [Edm93] proves a lower bound of T = Omega Gamma n 4=3 =S 1=3 ) However, there is still a big gap ....

....our claim that the JAG (and hence the NNJAG) model is a reasonable structured model for graph connectivity problems. In Chapter 5, we give some evidence that stcon is not in SC and thus, that SC ( P Polylogspace. In particular, we improve the lower bounds of Barnes and Edmonds [Edm93, BE93] to T = 2 Omega Gamma log 2 (n log n=S) log log n ) Theta p nS= log n on the probabilistic NNJAG model. This is the first result proved on a 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 ....

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Greg Barnes and Jeff Edmonds. Time-space lower bounds for directed s-t connectivity on JAG models. In 34th Annual Symposium on Foundations of Computer Science, pages 228--237, Palo Alto, CA, November 1993.

....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 ....

....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 imply a polynomial lower bound on the computation time if no upper bounds are imposed in the space used by the computation. Given the current knowledge of the s t connectivity problem it seems unlikely that one can prove super polynomial lower bounds for a general class of graph exploration ....

G. Barnes and J. Edmonds. Time-space lower bounds for directed s--t connectivity on JAG models. Proc. 34th Symp. on Foundations of Computer Science, 228--237, 1993. 28

.... of a deterministic Turing machine by an alternating machine) and Paul, Pippenger, Szemeredi and Trotter [13] non deterministic linear time is not a subset of deterministic linear time) Time space lower bounds have also been shown for other models such as Jumping Automata for Graphs (JAG) [6, 1, 5], branching programs [12, 3, 2] and comparison models [16] 2 Preliminaries We will use the multi tape Turing machine model to prove the main theorem. Let N(t) and D(t) denote the classes of all languages accepted by Turing machines running in nondeterministic time O(t) and deterministic time ....

G. Barnes and J. A. Edmonds. Time-space lower bounds for directed st-connectivity on graph automata models. SIAM Journal on Computing, 27(4):1190--1202, Aug. 1998.

....will distinguish this nonjumping variant by referring to it as a WAG walking automaton for graphs . Following the preliminary appearance of some of these results [10] Edmonds [26] proved a much stronger result for traversing undirected graphs than that proved in [9] and Barnes and Edmonds [6] and Edmonds and Poon [27] proved even more dramatic tradeoffs for traversing directed graphs. The results described above have the strength that they hold independent of the magnitude of Q, the number of states. Presumably the bounds can be strengthened by also accounting for Q. It is tempting ....

G. Barnes and J. A. Edmonds. Time-space lower bounds for directed s-t connectivity on JAG models. In Proceedings 34th Annual Symposium on Foundations of Computer Science, pages 228--237, Palo Alto, CA, Nov. 1993. IEEE.

....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 ....

....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 imply a polynomial lower bound on the computation time if no upper bounds are imposed in the space used by the computation. Given the current knowledge of the s t connectivity problem it seems unlikely that one can prove superpolynomial lower bounds for a general class of graph exploration ....

G. Barnes and J. Edmonds, Time-space lower bounds for directed s--t connectivity on graph automata models, SIAM J. Comput., 27 (1998), pp. 1190--1202.

.... 1 = LOGCFL AC 1 NC 2 : The research on graph connectivity is voluminous and even since Wigderson s excellent survey of the state of the art in 1992 [17] there have been significant new developments in connectivity algorithms [4, 12] and lower bounds on restricted models of computation [11, 3, 10, 19]. The key tool in showing that every problem in NL may be solved with circuits of relatively small depth is the Repeated Squaring or Pointer Doubling algorithm for transitive closure. Another way of phrasing some of these complexity questions is to ask whether or not repeated squaring gives ....

Greg Barnes and Jeff A. Edmonds. Time-space lower bounds for directed s-t connectivity on JAG models. In Proceedings 34th Annual Symposium on Foundations of Computer Science, pages 228-- 237, Palo Alto, CA, November 1993. IEEE.

....preliminary version of this paper by Edmonds and Poon [EP95] a lower bound of T 2 2 Omega Gamma314 2 ( n log n S ) log log n) Theta (nS= log n) 1=2 was proved. Our result greatly improves the previous 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 ....

....a JAG due to the existence of polynomial length universal traversal sequences [AKL 79] Thus one cannot hope to get super polynomial time lower bounds for stcon by establishing similar bounds for ustcon. The first nontrivial lower bound explicitly for stcon was given by Barnes and Edmonds [BE93] They showed that ST 2 Omega Gamma n 2 = log n) on the JAG model. In fact their result was proved on a more powerful variant of JAG called many states, big step JAG which, unlike an ordinary JAG, is capable of traversing trees in O(log n) space. Using a proof technique completely different ....

[Article contains additional citation context not shown here]

Greg Barnes and Jeff Edmonds. Time-space lower bounds for directed s-t connectivity on JAG models. In 34th Annual Symposium on Foundations of Computer Science, pages 228--237, Palo Alto, CA, November 1993.

....edged connected to v i has label 1 move P 1 back into the tooth, down to the bottom, look for node t end if end for Every tooth is connected to some back node v i via the edge labeled 1. Therefore, every tooth will be traversed once and only once. 6. 2 Directed Graphs Recently Greg Barnes and I [BE93] increased the time space tradeoff for directed graphs from T Theta S 1 3 2 Omega i n 4 3 j to T Theta S 2 n 2 log O(1) n on a NNJAG. The techniques are similar to those in Chapter 4, but use a more complicated family of graphs. Although there are algorithms for undirected ....

Greg Barnes, Jeff Edmonds. Time-Space Lower Bounds for Directed s-t Connectivity on JAG Models To appear in 34st Annual Symposium on Foundations of Computer Science, Palo Alto, CA, Nov. 1993.

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Greg Barnes, Jeff Edmonds. Time-Space Lower Bounds for Directed s-t Connectivity on JAG Models In 34st Annual Symposium on Foundations of Computer Science, pages 228--237, Palo Alto, CA, Nov. 1993.

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