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41st Annual Symposium on Foundations of Computer Science
Entropy waves, the zigzag graph product, and new constantdegree expanders and extractors
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
O. Reingold, S. Vadhan, A. Wigderson, "Entropy waves, the zigzag graph product, and new constantdegree expanders and extractors," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 3, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892006, author = {O. Reingold and S. Vadhan and A. Wigderson}, title = {Entropy waves, the zigzag graph product, and new constantdegree expanders and extractors}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {3}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892006}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Entropy waves, the zigzag graph product, and new constantdegree expanders and extractors SN  02725428 SP EP A1  O. Reingold, A1  S. Vadhan, A1  A. Wigderson, PY  2000 KW  entropy; graph theory; eigenvalues and eigenfunctions; probability; entropy waves; zigzag graph product; constantdegree expanders; constantdegree extractors; probability distributions; constructive interference; explicit extractors; high minentropy sources; eigenvalue bound VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
The main contribution is a new type of graph product, which we call the zigzag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constantdegree expanders of every size, starting from one constantsize expander. Crucial to our intuition (and simple analysis) of the properties of this graph product is the view of expanders as functions which act as "entropy wave" propagatorsthey transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated. In these terms, the graph product affords the constructive interference of two such waves. A variant of this product can be applied to extractors, giving the first explicit extractors whose seed length depends (poly)logarithmically on only the entropy deficiency of the source (rather than its length) and that extract almost all the entropy of high minentropy sources. These high minentropy extractors have several interesting applications, including the first constantdegree explicit expanders which beat the "eigenvalue bound".
Index Terms:
entropy; graph theory; eigenvalues and eigenfunctions; probability; entropy waves; zigzag graph product; constantdegree expanders; constantdegree extractors; probability distributions; constructive interference; explicit extractors; high minentropy sources; eigenvalue bound
Citation:
O. Reingold, S. Vadhan, A. Wigderson, "Entropy waves, the zigzag graph product, and new constantdegree expanders and extractors," focs, pp.3, 41st Annual Symposium on Foundations of Computer Science, 2000
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