Lecture 7 : Expanders
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چکیده
In this lecture we give basic background about expander graphs. Expanders are graphs with strong connectivity properties: every two large subsets of vertices in an expander have many edges connecting them. Surprisingly, one can construct very sparse graphs that are expanders, and this is what makes them so useful. Expanders have a huge number of applications in theoretical computer science: in construction of fault-tolerant networks, in proofs of complexity-theoretic results like SL = L, in design of error correcting codes, etc. We use expanders to amplify the soundness of PCPs, and in subsequent lectures, to obtain PCPs with a constant number of queries.
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