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 | |
|---|---|
\({x}_{i}^{0}\) | \(=\left\{ {\begin{array}{*{20}{c}} 1 & {{\text{if the person}}\, i \, {\text{received a message at the initial time of the message diffusion,}}} \\ 0 & {{\text{otherwise;}}}\end{array}}\right.\) |
\({x}_{is}^{t}\) | \(=\left\{{\begin{array}{*{20}{c}}1 & {{\text{if the person}}\, i \, {\text{received a message at time period}} \, t \, {\text{in scenario}} \, s (t=1,\dots ,T),}\\ 0 &{\text{otherwise;}}\end{array}}\right.\) |
\({l}_{ijs}^{t}\) | \(=\left\{{\begin{array}{*{20}{c}} 1 & {{\text{if the person}}\, i \, {\text{forward the message to the person}}\, j \, {\text{at period}} \, t \, {\text{in scenario}} \, s,}\\ 0 & {{\text{otherwise;}}}\end{array}}\right.\) |