Exploring a QoS Driven Scheduling Approach for Peer-to-Peer Live Streaming Systems with Network Coding

Table 1

Transformation rules.

Transformation rules of vertexes
(1)	We add two virtual vertexes, source vertex 𝑆 and terminal vertex 𝑇.
(2)	We add |𝑁𝐵𝑅| parent vertexes, each of which is represented by 𝑝𝑖, 𝑖 ∈ 𝑁𝐵𝑅.
(3)	We add the vertex 𝑠𝑠𝑗 to express the substream 𝑗, 𝑗 ∈ {1,2,…,𝑁^′}.
(4)	We add the vertex 𝐶 to express the child node, which makes the scheduling strategy.
Transformation rules of edges
(5)	We add the edge between vertex 𝑆 and vertex 𝑝𝑖, the cost of which is 0 and capacity of which is 𝑜𝑖.
(6)	For ∀𝑗 ∈ {1,2,…,𝑁^′}, if ℎ(𝑖,𝑗) = 1, we add the edge between the vertex 𝑝𝑖 and vertex 𝑠𝑠𝑗, the cost of which is 𝐶(𝑖,𝑗) and the capacity of which is 1.
(7)	For ∀𝑗 ∈ {1,2,…,𝑁^′}, we add the edge between the vertex 𝑠𝑠𝑗 and the vertex 𝐶, the cost of which is 0 and the capacity of which is 1.
(8)	We add the edge between vertex 𝐶 and vertex 𝑇, the cost of which is 0 and capacity of which is 𝑁.