COMS 4995 : Introduction to Coding Theory
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چکیده
Informally, an expander is an undirected graph that has relatively sparse density, but whose vertices are nevertheless highly connected. Consequently, expanders have the property that any small subset of the vertices has a large set of neighbors outside of the set. This simple graph property has led to highly useful results in a number of branches of computer science. In addition, the study of expansion properties of graphs in and of itself has proven to be quite a rich field both in theoretical content, and in result applicability. Expander graphs have uses ranging from complexity theory and algorithm derandomization to coding theory and efficient network design. Although it has been proven that a random graph of constant degree at least 3 is an expander with high probability, many of the results in the fields above require an efficiently computable explicit method of construction of infinite families of growing size expanders.
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