Till Tantau

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 ...
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Till Tantau

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 ...
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Don Coppersmith, Lisa Fleischer, Atri Rudra

We consider the following simple algorithm for feedback arc set problem in weighted tournaments --- order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of $5$ if the weights satisfy \textit{probability constraints}

(for any pair of vertices $u$ and $v$, $w_{uv}+w_{vu}=1$). Special cases ...
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