Encodings of Multicast Trees

IEEE Transactions on Communications, 2011

2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record, 2000

2003

Journal of Combinatorial Theory, Series A, 2009

Lecture Notes in Computer Science, 2001

Lecture Notes in Computer Science, 2002

Proceedings of the fifteenth annual …, 2003

2012 9th International Conference on Fuzzy Systems and Knowledge Discovery, 2012

The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e.g., the time complexity, the required number of encoding links, and the required field size for a linear code solution. However, these issues as well as the solvability are less understood for networks with multiple multicast sessions. Recently, Wang and Shroff showed that the solvability of networks with two unit-rate multicast sessions (2-URMS) can be decided in polynomial time . In this paper, we prove that for the 2-URMS networks: 1) the solvability can be determined with time O(|E|); 2) a solution can be constructed with time O(|E|); 3) an optimal solution can be obtained in polynomial time; 4) the number of encoding links required to achieve a solution is upper-bounded by max{3, 2N -2}; and 5) the field size required to achieve a linear solution is upper-bounded by max{2, ⌊ 2N -7/4 + 1/2⌋}, where |E| is the number of links and N is the number of sinks of the underlying network. Both bounds are shown to be tight.

Compositio Mathematica, 2001