Polynomial-Time Construction of Linear Network Coding

Constructing kindependent sessions between ksource-sink pairs with the help of a linear operation at each vertex is one of the most standard problems in network coding. For an unbounded k, this is known to be NP-hard. Very recently, a polynomial-time algorithm was given for k= 2 [Wang and Shroff, ISIT 2007], but was open for a general (constant) k. This paper gives a polynomial-time algorithm for this problem under the assumption that the size of the finite field for the linear operations is bounded by a fixed constant.

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