Expansion Of Product Replacement Graphs

Authors:
Alexander Gamburd;Igor Pak
Affiliations:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA;Department of Mathematics, MIT, Cambridge, MA 02139, USA
Venue:
Combinatorica
Year:
2006

Citing 0
Cited 2

Polynomial-time theory of matrix groups

Proceedings of the forty-first annual ACM symposium on Theory of computing
Finite groups and complexity theory: from leningrad to saint petersburg via las vegas

CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We establish a connection between the expansion coefficient of the product replacement graph Γk(G) and the minimal expansion coefficient of a Cayley graph of G with k generators. In particular, we show that the product replacement graphs Γk(PSL(2,p)) form an expander family, under assumption that all Cayley graphs of PSL(2,p), with at most k generators are expanders. This gives a new explanation of the outstanding performance of the product replacement algorithm and supports the speculation that all product replacement graphs are expanders [42,52].