We present a deterministic algorithm running in space
O((log^2 n)/loglog n) solving the connectivity problem
on strongly unambiguous graphs. In addition, we present
an O(log n) time-bounded algorithm for this problem
running on a parallel pointer machine.
For a directed graph $G = (V, E)$, we say that a weight function $\rho \colon E \to [M]$ is *min-isolating* if the minimum-weight path from $u$ to $v$ is unique for each pair of vertices $u, v \in V$ such that $v$ is reachable from $u$. If we could ... more >>>
One of the central questions in space complexity is whether nondeterministic logspace computations (NL) can be simulated in unambiguous logspace (UL). A stronger notion, reach unambiguity (RUL $\subseteq$ UL $\cap$ coUL), requires every configuration reachable from the start to have exactly one computation path (Buntrock et.al. 91). While directed graph ... more >>>
