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TimeSpace Lower Bounds for Directed st Connectivity on JAG Models (Extended Abstract)
, 1993
"... Directed st connectivity is the problem of detecting whether there is a path from a distinguished vertex s to a distinguished vertex t in a directed graph. We prove timespace lower bounds of ST = \Omega\Gamma n 2 = log n) and S 1=2 T = \Omega\Gamma mn 1=2 ) for Cook and Rackoff's JAG ..."
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Cited by 9 (2 self)
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Directed st connectivity is the problem of detecting whether there is a path from a distinguished vertex s to a distinguished vertex t in a directed graph. We prove timespace lower bounds of ST = \Omega\Gamma n 2 = log n) and S 1=2 T = \Omega\Gamma mn 1=2 ) for Cook and Rackoff's JAG model [8], where n is the number of vertices and m the number of edges in the input graph, and S is the space and T the time used by the JAG. We also prove a timespace lower bound of S 1=3 T = \Omega\Gamma m 2=3 n 2=3 ) on the more powerful nodenamed JAG model of Poon [13]. These bounds approach the known upper bound of T = O(m) when S = \Theta(n log n).
On the Complexity of the stConnectivity Problem
, 1996
"... The directed stconnectivity problem is fundamental to computer science. There are many applications which require algorithms to solve the problem in small space and preferably in small time as well. Furthermore, its space and timespace complexities are related to several longstanding open probl ..."
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Cited by 6 (3 self)
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The directed stconnectivity problem is fundamental to computer science. There are many applications which require algorithms to solve the problem in small space and preferably in small time as well. Furthermore, its space and timespace complexities are related to several longstanding open problems in complexity theory. Depth and breadthfirst search are well known algorithms that solve the problem in optimal (i.e., O(n m)) time while using O(n log n) space where n and m are the number of nodes and edges in the graph respectively. It can also be solved in O(log 2 n) space and 2 O(log 2 n) time by Savitch's algorithm. For space S between \Theta(log 2 n) and \Theta(n log n), the best running time is T = 2 O(log 2 (n log n=S)) \Theta mn due to Barnes et al.. Establishing matching lower bounds on the Turing machine model ha...
Tight lower bounds for stconnectivity on the NNJAG model
 SIAM J. on Computing
, 1999
"... Abstract. Directed stconnectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Compu ..."
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Cited by 6 (1 self)
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Abstract. Directed stconnectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space lower bound on the probabilistic NNJAG model of Poon [Proc. 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 218–227]. Let n be the number of nodes in the input graph and S and T be the space and time used by the NNJAG, respectively. We show that, for any δ>0, if an NNJAG uses space S ∈ O(n1−δ), then T ∈ 2Ω(log2 (n/S)) ; otherwise n log n) / log log n) S
TimeSpace TradeOffs For Undirected STConnectivity on a JAG
"... The following is a second proof of (basically) the same undirected stconnectivity result using recursive flyswatters as given in my thesis and in STOC93 [Ed93a, EdPHD]. The input graph and the reduction techniques in the two proofs are similar. The main difference is that JAG result is reduced to ..."
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The following is a second proof of (basically) the same undirected stconnectivity result using recursive flyswatters as given in my thesis and in STOC93 [Ed93a, EdPHD]. 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 conjecture is that the player cannot get the pebble across the line much faster than that done by a random walk. Likely, however, this is hard to prove. What can be proven is that this game becomes equivalent to the game in the original paper, if the player who is directing the pebble always knows where in the line pebble is. Therefore, the lower bound for the original game applies to this new game. Hence, the JAG lower bound proved in this paper is the same as that proven before. Two advantages of this new proof are that it is a litt...