Abstract
Constructing k independent sessions between k source-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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Iwama, K., Nishimura, H., Paterson, M., Raymond, R., Yamashita, S. (2008). Polynomial-Time Construction of Linear Network Coding. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_23
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DOI: https://doi.org/10.1007/978-3-540-70575-8_23
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