Table 1 Summary of Symbols and Notations
From: Effective and scalable methods for graph protection strategies against epidemics on dynamic networks
Notation | Definition and description |
|---|---|
GD=(VD,ED) | dynamic network GD with the node set VD and the edge set ED |
G t | snapshot of dynamic network GD at time t |
k | protection budget, i.e., the number of nodes in graph GD that can be protected |
S | set of k nodes selected for protection |
N | number of nodes in graph GD |
M | number of edges in graph GD |
β | infection rate |
δ | recovery rate |
θ | ratio of surviving nodes in graph GD at the end of epidemics |
w(u,v) | edge weight between node u and v |
V c | vertex cover of graph Gt |
\(V_{c}^{*}\) | minimum vertex cover of graph Gt |
\(\mathbb {S}\) | current partial solution, set of selected \(V_{c}^{*}\) nodes of graph Gt |
d | size of embedding vector dimension |
\(h(\mathbb {S})\) | feature-based representation of \(\mathbb {S}\) in d-dimensional vector |
B | batch samples of training |
\(\mathbb {M}\) | experience replay memory of n-step fitted Q-Learning |
ψ i | set of neural network parameters (weights) of respective embedding variable i |
Ψ | collection of neural network’s set of parameters (weights) \(\Psi = \{\psi _{i}\}_{i=1}^{7}\) |