From: Efficient computation of optimal temporal walks under waiting-time constraints
ℕ | the natural numbers (including 0) {0,…} |
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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 \(\beta : V \rightarrow \mathbb{N}\) |
V_{t} | the vertex subset V_{t}⊆V at time t, that is, V_{t}:={v,w∣(v,w,t,λ)∈E} |
E_{t} | the time-arc subset at time t, that is, E_{t}:={(v,w)∣(v,w,t,λ)∈E} |
G_{t} | the directed static graph G_{t}:=(V_{t},E_{t}) |
(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 |