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Marvin Minsky said: The most important discovery since G&...
I will suggest the following books.
The Golden Ticket: P, NP, and the Search for the Impossible by Lance Fortnow.
The book is written for all kind of readers and doesn't require you to know anything about Theoretical Computer Science. It shows the disney world where P=NP.
The Nature of Computation by Cristopher Moore and Stephen Mertens. Deep ideas of ...
Expanders are special graph which are sparse yet highly connected. The challenge is to give an explicit construction of expanders. See the survey by Hoory-Linial-Wigderson-Expander Graphs and their Application for several applications of expanders.
The most useful expanders are the ones with constant degree.If we have constant-sized object then we can freely ...