Jeff Edmonds. Time-Space Lower Bounds for Undirected and Directed ST-Connectivity on JAG Models. PhD thesis, University of Toronto, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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 between the upper and lower bounds. In particular, the above results do not yield any superpolynomial lower bound on time T no matter how small the space S becomes. There are also other approaches to ....

....substantiates 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 ....

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Jeff Edmonds. Time-Space Lower Bounds for Undirected and Directed ST-Connectivity on JAG Models. PhD thesis, University of Toronto, 1993.

.... Trade Offs For Undirected ST Connectivity on a JAG Abstract The following is a second proof of (basically) the same undirected st connectivity result using recursive flyswatters as given in my thesis and in STOC 93 [Ed93a, Ed PHD]. The input graph and the reduction techniques in the two proofs are similar. The main difference is that JAG result is reduced to a different game. In this paper, the game consists of a pebble walking on a line. The movements of the pebble are directed by a player and a random input. The ....

....more complex games. To work on the conjecture one only needs to read the definition of Game 1 and Conjecture 1. Section 6 defines the flyswatter graph. It briefly outlines the Omega Gamma n 2 ) lower bound when the JAG has only one pebble. It also gives the intuition to my original proof in [Ed93a, Ed PHD]. Section 7 describes a line of fly swatter graphs and compares its complexity to that of the random walk game. Section 8 describes how the input graph is recursively built. Section 9 provides the definitions of the time, pebbles, and cost used at a particular level of the recursion. Section 10 ....

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J. A. Edmonds. Time-Space Lower Bounds for Undirected and Directed ST - Connectivity on JAG Models. PhD thesis, University of Toronto, Aug. 1993.

....be run on a JAG. It is interesting how close our lower bounds are to this upper bound. The current JAG lower bounds for ustcon are weak and only allow a small number of pebbles [13] Our hope is that the techniques used in this paper can be applied to the undirected version of s t connectivity. [12] discusses some ideas and di#culties in doing this. TIME SPACE LOWER BOUNDS 1201 Ultimately, one would like to prove lower bounds for stcon on a general model of computation. Any nontrivial bounds for general models would be a step in this direction. A more modest goal would be to add features ....

<F4.668e+05> J. A.<F3.811e+05> Edmonds,<F3.365e+05> Time-Space Lower Bounds for Undirected and Directed<F3.726e+05><F3.365e+05> ST-Connectivity on JAG<F3.811e+05> Models, Ph.D. thesis, Department of Computer Science, University of Toronto, Aug. 1993.

....showed that ST # ## 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 di#erent from [4] Edmonds [14] showed that S 1 3 T # ## n 4 3 ) on the NNJAG model. These results still do not yield superpolynomial lower bounds on time no matter how small S is. In view of this large gap between the upper and lower bounds and the fact that the Barnes et al. algorithm was obtained by combining several ....

....2 n log log n ) Poon [26] gives a stronger lower bound of T # 2 (2 ## log 2 n S) For example, when S # O(log n) his result implies that T # 2 n c for some constant c 0. 2260 JEFF EDMONDS, CHUNG KEUNG POON, AND DIMITRIS ACHLIOPTAS This paper borrows a lot of techniques from [14]. The bound is proved for the probabilistic NNJAG model by transforming the machine into a structured branching program, and applying a progress argument introduced by Borodin et al. 10] and also used in many proofs of time space trade o# lower bounds, including [8, 5, 9, 33] Roughly, the ....

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<F3.748e+05> J.<F3.815e+05> Edmonds,<F3.419e+05> Time-Space Lower Bounds for Undirected and Directed ST-Connectivity on JAG<F3.815e+05> Models, Ph.D. thesis, University of Toronto, Toronto, ON, Canada, 1993.

....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 of Omega Gamma 24 2 n) on the NNJAG model. No tight space lower bound was ....

....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 from [BE93] Edmonds [Edm93a] showed that S 1=3 T 2 Omega Gamma n 4=3 ) on the NNJAG model. These results still do not yield super polynomial lower bounds on time no matter how small S is. In view of this large gap between the upper and lower bounds and the fact that the Barnes et al. algorithm was obtained by combining ....

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Jeff Edmonds. Time-Space Lower Bounds for Undirected and Directed STConnectivity on JAG Models. PhD thesis, University of Toronto, 1993.

....bounds on these more general models. Acknowledgments We would like to thank Faith Fich for her extensive support, and Paul Beame, Al Borodin, Russell Impagliazzo, and Hisao Tamaki for their helpful comments and suggestions. An earlier version of some of this work appears in Edmonds s PhD thesis [10]. ....

J. A. Edmonds. Time-Space Lower Bounds for Undirected and Directed ST-Connectivity on JAG Models. PhD thesis, University of Toronto, Aug. 1993.

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