From: Effective and scalable methods for graph protection strategies against epidemics on dynamic networks
Notation | Definition and description |
---|---|
G^{D}=(V^{D},E^{D}) | dynamic network G^{D} with the node set V^{D} and the edge set E^{D} |
G _{ t} | snapshot of dynamic network G^{D} at time t |
k | protection budget, i.e., the number of nodes in graph G^{D} that can be protected |
S | set of k nodes selected for protection |
N | number of nodes in graph G^{D} |
M | number of edges in graph G^{D} |
β | infection rate |
δ | recovery rate |
θ | ratio of surviving nodes in graph G^{D} at the end of epidemics |
w(u,v) | edge weight between node u and v |
V _{ c} | vertex cover of graph G_{t} |
\(V_{c}^{*}\) | minimum vertex cover of graph G_{t} |
\(\mathbb {S}\) | current partial solution, set of selected \(V_{c}^{*}\) nodes of graph G_{t} |
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) \(\Psi = \{\psi _{i}\}_{i=1}^{7}\) |