TITLE: Computionally efficient vertex enumeration for (convex) polytopes
QUESTION [8 upvotes]: Let $P \subseteq \mathbb{R}^d$ be an $\mathcal{H}$-polytope. The vertex enumeration problem asks for the set of vertices $V$ of $P$. Theoretically, the vertex enumeration problem for $P$ can be performed in $\mathcal{O}(|V|^{\lfloor d/2 \rfloor})$, cf. [1].
Practically, one would use the double description method, cf. [2], and cf. cddlib for an implementation of the former.
In my application, I have to solve a rather large number of such vertex enumeration problems in let's say dimension $10$. Unfortunately, ccdlib is too slow and causes numerical problems (the GMP version is even slower). 
Moreover, for my application it suffices to find a superset of $V$. Hence, I thought there might be a way to decompose $P$ into "simpler" polytopes such that the vertex enumeration for each such polytope could be performed much faster. 
Is anybody aware of such method?

REPLY [10 votes]: cddlib is rather old; a much more efficient implementation of the double description method is in PPL (Parma Polyhedra Library). One frontend to PPL can be found in Sagemath: http://www.sagemath.org/doc/reference/geometry/sage/geometry/polyhedron/constructor.html
PPL will perform computations exactly.
Apart from the double description there is the reverse search, a method consisting of "walking" over the vertices, implemented in lrs: http://cgm.cs.mcgill.ca/~avis/C/lrs.html
and it might work better for your problems.