A Survey of Linear Network Coding and Network Error Correction Code Constructions and Algorithms

Table 2

Comparison of deterministic algorithms for network code construction. |𝐸| is the total number of edges in the network, |𝑉| the number of nodes, and |𝑇| the number of sinks. ℳ(ℎ) is the time required to perform an ℎ×ℎ matrix multiplication. Langberg suggest that the correct running times of the algorithms of Jaggi et al. are different when the number of edges is small [16].

	Field size (q)	Time complexity
Yeung et al. [39], Algorithm 2.19	|𝐸|+ℎ−1ℎ−1	𝒪(|𝐸|)
Jaggi et al. [15] LIF	2|𝑇|	𝒪(|𝐸||𝑇|ℎ^2)
Jaggi et al. [15] DLIF	|𝑇|	𝒪(|𝐸||𝑇|ℎ(ℎ+|𝑇|))
Jaggi et al. [15] fast	2|𝐸||𝑇|	𝒪(|𝐸||𝑇|ℎ+|𝑇|ℳ(ℎ))
Langberg et al. [16]	|𝑇|	𝒪(|E||𝑇|^2ℎ+ℎ^4|𝑇|^3(|𝑇|+ℎ))
Harvey et al. [40]	|𝑇|	𝒪(|𝑇|ℎ^3logℎ)