Graph Connectivity and Network Coding
نویسندگان
چکیده
Graph Connectivity and Network Coding LEUNG, Kai Man Master of Philosophy Department of Computer Science and Engineering The Chinese University of Hong Kong 2011 In this thesis we present a new algebraic formulation to compute edge connectivities in a directed graph, using the ideas developed in network coding. This reduces the problem of computing edge connectivities to solving systems of linear equations, thus allowing us to use tools in linear algebra to design new algorithms. Using the algebraic formulation we obtain faster algorithms for computing single source edge connectivities and all pairs edge connectivities, in some settings the amortized time to compute the edge connectivity for one pair is sublinear. Through this connection, we have also found an interesting use of expanders and superconcentrators to design fast algorithms for some graph connectivity problems.
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