On the Solvability of 3s/nt Sum-Network---A Region Decomposition and Weak Decentralized Code Method
Abstract
We study the network coding problem of sum-networks with 3 sources and n terminals (3s/nt sum-network), for an arbitrary positive integer n, and derive a sufficient and necessary condition for the solvability of a family of so-called terminal-separable sum-network. Both the condition of terminal-separable and the solvability of a terminal-separable sum-network can be decided in polynomial time. Consequently, we give another necessary and sufficient condition, which yields a faster (O(|E|) time) algorithm than that of Shenvi and Dey ([18], (O(|E|^3) time), to determine the solvability of the 3s/3t sum-network. To obtain the results, we further develop the region decomposition method in [22], [23] and generalize the decentralized coding method in [21]. Our methods provide new efficient tools for multiple source multiple sink network coding problems.
Cite
@article{arxiv.1502.00762,
title = {On the Solvability of 3s/nt Sum-Network---A Region Decomposition and Weak Decentralized Code Method},
author = {Wentu Song and Kai Cai and Chau Yuen and Rongquan Feng},
journal= {arXiv preprint arXiv:1502.00762},
year = {2015}
}
Comments
41 pages. arXiv admin note: text overlap with arXiv:1401.3941