In the present paper we show some new complexity bounds for
the matching problem for special graph classes.
We show that for graphs with a polynomially bounded number
of nice cycles, the decision perfect matching problem is in
$SPL$, it is hard for $FewL$, and the construction ... more >>>

We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in $O(\log^3 n)$ time on $n^{O(\log^2 n)}$ processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the ... more >>>