Computation of best possible low degree expanders

Authors:
Stefan Hougardy;Ivo Köthnig
Affiliations:
Forschungsinstitut für Diskrete Mathematik, Universität Bonn, Lennéstr. 2, 53113 Bonn, Germany;Institut für Informatik, Humboldt-Universität zu Berlin, 10099 Berlin, Germany
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

We present an algorithm for computing a best possible bipartite cubic expander for a given number of vertices. Such graphs are needed in many applications and are also the basis for many results in theoretical computer science. Known construction methods for expander graphs yield expanders that have a fairly poor expansion compared to the best possible expansion. Our algorithm is based on a lemma which allows to calculate an upper bound for the expansion of cubic bipartite graphs.