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TIGHT LOWER BOUNDS FOR st-CONNECTIVITY ON THE NNJAG MODEL
 

Summary: TIGHT LOWER BOUNDS FOR st-CONNECTIVITY ON THE
NNJAG MODEL
JEFF EDMONDS, CHUNG KEUNG POON, AND DIMITRIS ACHLIOPTAS§
SIAM J. COMPUT. c 1999 Society for Industrial and Applied Mathematics
Vol. 28, No. 6, pp. 2257­2284
Abstract. Directed st-connectivity 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. 218­227]. 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 > 0, if an NNJAG uses space S O(n1-), then T 2(log2
(n/S)); otherwise
T 2(log2
(
n log n
S
)/ log log n)
× (nS/ log n)1/2. (In a preliminary version of this paper by Edmonds
and Poon [Proc. 27th Annual ACM Symposium on Theory of Computing, Las Vegas, NV, 1995, pp.
147­156.], a lower bound of T 2(log2

  

Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz

 

Collections: Computer Technologies and Information Sciences