Deciding whether a vertex in a graph is reachable from another
vertex has been studied intensively in complexity theory and is
well understood. For common types of graphs like directed graphs,
undirected graphs, dags or trees it takes a (possibly
nondeterministic) logspace machine to decide the reachability
problem, and ... more >>>

This paper introduces logspace optimisation problems as
analogues of the well-studied polynomial-time optimisation
problems. Similarly to them, logspace
optimisation problems can have vastly different approximation
properties, even though the underlying existence and budget problems
have the same computational complexity. Numerous natural problems
are presented that exhibit such a varying ... more >>>

The reachability problem for graphs cannot be described, in the
sense of descriptive complexity theory, using a single first-order
formula. This is true both for directed and undirected graphs, both
in the finite and infinite. However, if we restrict ourselves to
graphs in which a certain graph parameter is fixed ... more >>>

We show that the reachability problem for directed graphs
that are either K_{3,3}-free or K_5-free
is in unambiguous log-space, UL \cap coUL.
This significantly extends the result of Bourke, Tewari, and Vinodchandran
that the reachability problem for directed planar graphs
is in UL \cap coUL.

Our algorithm decomposes ... more >>>

Designing algorithms that use logarithmic space for graph reachability problems is fundamental to complexity theory. It is well known that for general directed graphs this problem is equivalent to the NL vs L problem. For planar graphs, the question is not settled. Showing that the planar reachability problem is NL-complete ... more >>>

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 >>>