Preferential attachment definition
Preferential attachment. [12] means a new node is more likely to connect to heavily linked nodes when it joins the network. The BA model has some disadvantages as the growth model for the overlay topology of P2P networks. Firstly, it does not provide hard cut-offs. Since a heavily linked node uses a lot of bandwidth in P2P networks, nodes usually are not willing to maintain high degrees. For this reason, a user-defined hard cut-off (i.e. the maximum) degree is imposed lower than the natural cut-off arising in the BA model. The imposed hard cut-offs restrict the feasible overlays to the limited scale-free topologies, which are more practical. Moreover, the BA model also requires the global information about the topology to add connections when a new node joins. In real-world applications, however, the communication cost of obtaining the global information is prohibitive. Therefore, a distributed approach that constructs the topology without global information is desired. In [6], authors study the construction of limited scale-free overlay topolo- gies for unstructured peer-to-peer networks. In the Hop-and-Attempt Pref- erential Attachment (HAPA) algorithm [6], a new node joining the network connects to k (i.e. the minimum degree) nodes in a random route starting from a randomly chosen node. This scheme works because high degree nodes are more likely to occur in a random route than nodes with low degree. The hard cut-off is used to avoid ”superhubs”, which are nodes with degrees linear to the network size. HAPA algorithm produces the topologies with degree distribution approximately following the power-law with scaling parameter
Preferential attachment. The probability ∏ that the new processor (PE) is connected to processor Pi depends on the degree ki of processor Pi, such that ∏ ( k i ) = ∑ j k j …………………………………………(1) : The newly introduced TMs at time t + 1 PA The newly introduced PB D processor PE at time t + 1 P : Processor : Host processor PE PC