TY - JOUR
T1 - Randomness conductors and constant-degree lossless expanders
AU - Capalbo, Michael
AU - Reingold, Omer
AU - Vadhan, Salil
AU - Wigderson, Avi
PY - 2002
Y1 - 2002
N2 - 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 = ε) D, where D is the degree and ε 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 method cannot give better bounds. The main abstract contribution 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.
AB - 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 = ε) D, where D is the degree and ε 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 method cannot give better bounds. The main abstract contribution 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.
UR - http://www.scopus.com/inward/record.url?scp=0036041924&partnerID=8YFLogxK
U2 - 10.1145/510002.510003
DO - 10.1145/510002.510003
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AN - SCOPUS:0036041924
SN - 0734-9025
SP - 659
EP - 668
JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing
JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing
T2 - Proceedings of the 34th Annual ACM Symposium on Theory of Computing
Y2 - 19 May 2002 through 21 May 2002
ER -