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Table 1 Frequently used notation

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