3s/nt和网络的可解性--区域分解与弱分散编码方法
On the Solvability of 3s/nt Sum-Network---A Region Decomposition and Weak Decentralized Code Method
摘要：
研究了具有任意正整数n的3源n端和网络（3s/nt和网络）的网络编码问题，得到了一类所谓端可分和网络可解的充要条件.终端可分和网络的终端可分条件及终端可分和网络的可解性都可以在多项式时间内确定。因此，我们给出了另一个充分必要条件，它比Shenvi和Dey的算法（[18]，（O（|E| ^3）时间）更快（O（|E|）时间），以确定3s/3 t和网络的可解性。为了得到这些结果，我们进一步发展了[22]，[23]中的区域分解方法，并推广了[21]中的分散编码方法。我们的方法为多源多汇网络编码问题提供了新的有效工具。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
