From: Non-submodular model for group profit maximization problem in social networks
Notation | Description |
---|---|
\(G=(V,E,P)\) | A social network with user set V and edge set E. P is the influence probability. \(P_e\) represents influence probability on edge e where \(0\le P_e\le 1\) |
\(G=(V,C,E,P,f)\) | A candidate seed set \(C\subseteq V\). Each user has a weight f |
\({\mathcal {U}}\) | The set of groups, b(U) is the benefit when U is activated for \(U\in {\mathcal {U}}\) |
\(c(v)\ge 0\) | c(v) is the cost to activate v |
\(n=|V|\) | The number of users |
\(m=|E|\) | The number of edges |
\(l=|{\mathcal {U}}|\) | The number of groups |
\(\beta\) | The threshold of a group being activated, \(0<\beta \le 1\) |
k | The number of seeds |
\(\beta (S)\) | The expected benefit of all activated groups with seed set S. |
\(\gamma (S)\) | The expected diffusion cost of all activated users with seed set S |
\(\rho (S)=\beta (S)-\gamma (S)\) | The expected profit with seed set S |