Randomness conductors and constant-degree lossless expanders

Michael Capalbo, Omer Reingold, Salil Vadhan, Avi Wigderson
2002 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02  
The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: (1 − ǫ)D, where D is the degree and ǫ is an arbitrarily small constant. The best previous explicit constructions gave expansion factor D/2, which is too weak for many applications. The D/2 bound was obtained via the eigenvalue method, and is known that that method cannot give better bounds. The main abstract
more » ... ution of this paper is the introduction and initial study of randomness conductors, a notion which generalizes extractors, expanders, condensers and other similar objects. In all these functions, certain guarantee on the input "entropy" is converted to a guarantee on the output "entropy". For historical reasons, specific objects used specific guarantees of different flavors. We show that the flexibility afforded by the conductor definition leads to interesting combinations of these objects, and to better constructions such as those above. * A full version of this paper will be posted on the Electronic Colloquium on Computational Complexity,
doi:10.1145/510002.510003 fatcat:zrdsw422zbdtpowpnj6a4lgs3e