MPI-INF/SWS Research Reports 1991-2021

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

Barnes, Greg and Edmonds, J. A.

April 1994, ? pages.

Status: available - back from printing

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},