Table 1 Frequently used notation for a temporal graph \(\mathcal {G}\). The first part shows global variables, the second part shows frequently used local variables
From: Efficient computation of optimal temporal walks under waiting-time constraints
ℕ | the natural numbers (including 0) {0,…} |
|---|---|
V | the vertex set of \(\mathcal {G}\) |
E | the time-arc set of \(\mathcal {G}\) |
[T] | the time interval of \(\mathcal {G}\) |
α | the minimum waiting time with \(\alpha : V \rightarrow \mathbb{N}\) |
β | the maximum waiting time with \(\beta : V \rightarrow \mathbb{N}\) |
Vt | the vertex subset Vt⊆V at time t, that is, Vt:={v,w∣(v,w,t,λ)∈E} |
Et | the time-arc subset at time t, that is, Et:={(v,w)∣(v,w,t,λ)∈E} |
Gt | the directed static graph Gt:=(Vt,Et) |
(v,w,t,λ) | a time-arc from u to v with time stamp t and transmission time λ |
k | usually the number of time-arcs in an optimal walk |
P | a walk; often \(P = \left (\left (v_{i-1},v_{i},t_{i},\lambda _{i} \right)\right)_{i=1}^{k}\) indicates the optimal walk |