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Table 1 Notation, variables, and parameters used in the DDIP model

From: Robust communication network formation: a decentralized approach

VariableDefinition
\(V=\{1,2,\ldots,n\}\)Set of actors in the network
\(|V|=n\)The number of actors in the network
\(P_i\)Set of actors in the proximity of actor i
tTime period
\(t_{{\text{max}}}\)The maximum number of periods to run the DDIP model
\(O_{i}^{t}\)The set of actor i’s out-directed neighbors at period t
\(I_{i}^{t}\)The set of actor i’s in-directed neighbors at period t
\(g_{i}^{t}\)The local network structure of actor i at period t
mThe number of messages each actor sends per period t
\(p_{ijk}^{t}\)The fraction of messages actor i receives from source j through neighbor k during period t
\(\alpha\)The probability of a message being terminated
\(\beta _{ij}^{{\text{own}},t}\)Actor i’s own (personal) preference for messages from actor j, during period t
\(\beta _{ij}^{{\text{neigh}},t}\)The average preference of actor i’s out-directed neighbors for messages from actor j during period t
\(\beta _{ij}^{{\text{total}},t}\)The overall preference that actor i has for messages from actor j at time t
\(\rho\)Preference parameter: The weight of an actor’s own preferences against it’s neighbors preferences
\(\gamma\), wCost parameters: the weights in the objective