Is the new Cramer's rule algorithm really as good as LU?

The Wikipedia article on Cramer's rule cites a recent paper that claims to have an O(n^3) algorithm:

Ken Habgood and Itamar Arel. 2010. Revisiting Cramer's rule for solving dense linear systems. In Proceedings of the 2010 Spring Simulation Multiconference (SpringSim '10). ACM, New York, NY, USA, Article 82

Available at:

http://dl.acm.org/citation.cfm?id=1878623

Unfortunately subscription is required so would anyone with access kindly be able to explain what is the main trick that is used?

In particular, how do they avoid calculating (n+1) determinants of O(n^3) complexity each, and how does the accuracy compare with LU/PLU?

[Gareth]

They use Chio condensation - and a variant of this. The habgood thesis is online and contains the same info.