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Time-space lower bounds for directed s-t connectivity on JAG models

Barnes, Greg and Edmonds, J. A.

MPI-I-94-119. April 1994, ? pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
Directed $s$-$t$ 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 time-space lower bounds of $ST = \Omega(n^{2}/\log n)$
and $S^{1/2}T = \Omega(m n^{1/2})$
for Cook and Rackoff's JAG model, 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 time-space lower bound of
$S^{1/3}T = \Omega(m^{2/3}n^{2/3})$
on the more powerful
node-named JAG model of Poon.
These bounds approach the known upper bound
of $T = O(m)$
when $S = \Theta(n \log n)$.
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  AUTHOR = {Barnes, Greg and Edmonds, J. A.},
  TITLE = {Time-space lower bounds for directed s-t connectivity on JAG models},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-119},
  MONTH = {April},
  YEAR = {1994},
  ISSN = {0946-011X},