Skip to main content

Table 1 The notations which are used to formulate the problem

From: A robust optimization model for influence maximization in social networks with heterogeneous nodes

Sets and indices
\(i,j\) Index of source and destination persons \(i,j=1,\dots ,n;\)
\(t\) Index of discrete time periods \(t=\mathrm{0,1},\dots ,T;\)
\(s\) Index of scenarios \(s=1,\dots ,S;\)
\({N}_{i}\) Out-degree of person i (i.e., the persons that \(i\) has their phone number in her contact list);
\({K}_{i}\) In-degree of person i (i.e., the persons that have \(i\)’s phone number in their contact list)
Parameters
\({a}_{ijs}\) Binary parameter representing that the message may be forwarded by the person \(i\) to the person \(j\) in scenario \(s;\)
\({\pi }_{s}\) Probability of scenario \(s;\)
M An adequate large number
Variables
\({x}_{i}^{0}\) \(=\left\{ {\begin{array}{*{20}{c}} 1 & {{\text{if the person}}\, i \, {\text{received a message at the initial time of the message diffusion,}}} \\ 0 & {{\text{otherwise;}}}\end{array}}\right.\)
\({x}_{is}^{t}\) \(=\left\{{\begin{array}{*{20}{c}}1 & {{\text{if the person}}\, i \, {\text{received a message at time period}} \, t \, {\text{in scenario}} \, s (t=1,\dots ,T),}\\ 0 &{\text{otherwise;}}\end{array}}\right.\)
\({l}_{ijs}^{t}\) \(=\left\{{\begin{array}{*{20}{c}} 1 & {{\text{if the person}}\, i \, {\text{forward the message to the person}}\, j \, {\text{at period}} \, t \, {\text{in scenario}} \, s,}\\ 0 & {{\text{otherwise;}}}\end{array}}\right.\)