The paper presents a simple construction of polynomial length universal
traversal sequences for cycles. These universal traversal sequences are
log-space (even $NC^1$) constructible and are of length $O(n^{4.03})$. Our
result improves the previously known upper-bound $O(n^{4.76})$ for
log-space constructible universal traversal sequences for cycles.
For every $\epsilon>0$,
we present a {\em deterministic}\/ log-space algorithm
that correctly decides undirected graph connectivity
on all but at most $2^{n^\epsilon}$ of the $n$-vertex graphs.
The same holds for every problem in Symmetric Log-space (i.e., $\SL$).
Making no assumptions (and in particular not assuming the ... more >>>
We highlight a common theme in four relatively recent works
that establish remarkable results by an iterative approach.
Starting from a trivial construct,
each of these works applies an ingeniously designed
sequence of iterations that yields the desired result,
which is highly non-trivial. Furthermore, in each iteration,
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We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let ${\cal G}(m,g)$ be the class of directed acyclic graphs with $m = m(n)$ source vertices embedded on a surface (orientable or non-orientable) of genus $g = g(n)$. We give a log-space reduction that ... more >>>
A curious property of randomized log-space search algorithms is that their outputs are often longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the output or randomness verbatim? Running the algorithm again with new random bits ... more >>>
