J. A. Edmonds. Time-space trade-offs for undirected ST -connectivity on a JAG. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....since the families of regular graphs mentioned above have degree d = 1) and hence m = n) 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 ....

....In time 2(d) this has touched all 2(d) connecting edges incident to that entry vertex, which was impossible in the construction above. 22 4. Open Problem The obvious important problem is to strengthen and generalize these lower bounds. Following an earlier version of this paper [9] Edmonds [21] proved a much stronger time space tradeoff on general JAGs: for every z 2, a JAG with at most 28z log n log log n pebbles and at most 2 states requires time n 1 2 Omega1 log n) log log n) to traverse 3 regular graphs. The ultimate goal might be to prove that ST = Omega# mn) for JAGs, ....

J. A. Edmonds. Time-space trade-offs for undirected ST -connectivity on a JAG. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.

.... 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 ....

Jeff A. Edmonds. Time-space tradeoffs for undirected st-connectivity on a graph automata. SIAM Journal on Computing, 27(5):1492--1513, October 1998.

....In [BBRRT] a lower bound of Omega Gamma n 2 ) is proved for a model that allows for an initial phase of distributing landmarks, but requires that the pebble takes deterministic walks on the graph, rather than random walks. Lower bounds on other variants of the JAG model are presented in [BBRRT, edmonds]. In particular, Edmonds [edmonds] allows for randomized algorithms, and proves that when the number of pebbles is sublogarithmic, the time to decide USTCON is superlinear (on the JAG model of computation) The main part of our paper is concerned with the analysis of the short term behavior of ....

....n 2 ) is proved for a model that allows for an initial phase of distributing landmarks, but requires that the pebble takes deterministic walks on the graph, rather than random walks. Lower bounds on other variants of the JAG model are presented in [BBRRT, edmonds] In particular, Edmonds [edmonds] allows for randomized algorithms, and proves that when the number of pebbles is sublogarithmic, the time to decide USTCON is superlinear (on the JAG model of computation) The main part of our paper is concerned with the analysis of the short term behavior of random walks, as this governs the ....

J. Edmonds. "Time-Space Tradeoffs For Undirected ST-Connectivity on a JAG". In Proc. of 25th Symposium of the Theory of Computing, 718--727, 1993.

.... 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 ....

J. A. Edmonds. Time-space tradeoffs for undirected st- connectivity on a graph automata. SIAM Journal on Computing, 27(5):1492--1513, Oct. 1998.

....nonjumping model is closer to the one studied by Blum and Sakoda [13] Blum and Kozen [12] and Hemmerling [30] We 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 ....

....(based on Broder et al. 20] and Barnes and Feige [7] cannot be made both errorless and substantially faster. We also showed that our lower bound is tight. The obvious important problem is to strengthen and generalize these lower bounds. Following an earlier version of this paper [10] Edmonds [26] proved a time space tradeoff on general JAGs: for every z 2, a JAG with at most 1 28z log n log log n pebbles and at most 2 log z n states requires time n Delta 2 Omega Gamma9144 n) log log n) to traverse 3 regular graphs. The ultimate goal might be to prove that ST = ....

J. A. Edmonds. Time-space trade-offs for undirected ST -connectivity on a JAG. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.

.... 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 ....

Jeff A. Edmonds. Time-space trade-offs for undirected ST -connectivity on a JAG. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.

....path between two designated nodes in any n node graph. JAGs have been used primarily to prove space efficiency for st connectivity algorithms, and they have recently resurfaced as a tool for analyzing time and space tradeoffs for graph traversal and connectivity problems (e.g. BB 90, Poo93, Edm93] Universal traversal sequences have been used to provide upper and lower bounds for the exploration of undirected graphs. Certainly, a universal traversal sequence for the class of directed graphs could be used to learn individual graphs. However, for arbitrary directed graphs with n nodes, a ....

Jeff Edmonds. Time-space trade-offs for undirected st-connectivity on a JAG. In Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.

....that S 2 Omega Gamma log 2 n log log n log log T ) for any coin flipping probabilistic NNJAG with space S and expected time T . Regarding the time space tradeoff, there are many lower bounds proved for ustcon on various weaker variants of the JAG model [BBR 90, BRT92, CR80] Edmonds [Edm93b] was the first to prove a time space lower bound for ustcon on the regular JAG model (with bounded space) All these results apply to (directed) stcon, which contains ustcon as a special case. However, ustcon appears to be easier than stcon both in terms of space and time space complexity. For ....

....and hence a number of new techniques are required to overcome this. In addition, the argument is applied recursively yielding a substantially greater lower bound than what would be possible without recursion. We note that similar recursive techniques have also been used in [CR80, BS83, Yao88, Edm93b, Poo93] 1.3 Organization of this paper We first define the NNJAG model in Section 2. In Section 3, we give the statement of our main result and its corollaries. In Sections 4 and 5, we describe the families of graphs used to defeat the NNJAG. In Section 6, we define a notion of progress for ....

Jeff Edmonds. Time-space trade-offs for undirected st-connectivity on a JAG. In Proceedings of the Twenty Fifth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.

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Jeff Edmonds. Time-space trade-offs for undirected st-connectivity on a JAG. In Proceedings of the Twenty Fifth Annual ACM Symposium on Theory of Computing, page 718-727, San Diego, CA, May 1993.

....space needed when using certain natural approaches to solve stcon. Many time space lower bounds have been proved for undirected s t connectivity on various weak versions of the JAG model [2, 7, 8] Edmonds was the first to prove a time space lower bound for ustcon on the unrestricted JAG model [9]. The standard algorithms for s t connectivity, 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 ....

....to get such a bound, one would probably have to devise techniques that take into account both the number of states and the number of pebbles. Second, one should be able to prove a similar bound on undirected graphs the current JAG lower bounds for ustcon allow only a small number of pebbles [9]. Ultimately, one would like to prove lower bounds for stcon like those presented above on a general model of computation. Any nontrivial bounds for general models would be a step in this direction. Another, less modest goal would be to add features to the NNJAG to make it more general (as Poon ....

J. Edmonds. Time-space trade-offs for undirected ST -connectivity on a JAG. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 718--727, San Diego, CA, May 1993.

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Jeff Edmonds. Time-space trade-offs for undirected st-connectivity on a JAG. In Proceedings of the Twenty Fifth Annual ACM Symposium on Theory of Computing, page 718-727, San Diego, CA, May 1993.

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