A robust information source estimator with sparse observations

Computational Social Networks

Table 1 Notation table

	Description
q _uv	The probability an infected node u infects its neighbor node v
p _v	The probability an infected node v recovers
Y	The partial snapshot
X_v(t)	The state of node v at time t
X(t)	The states of all nodes at time t
X[ 0,t]	The sample path from 0 to t
$X (t)$	The set of all valid sample paths from time slot 0 to t
$I_{Y}$	The set of the observed infected nodes
$ℋ_{Y}$	The set of the unobserved nodes
$\tilde{e} (v, I_{Y})$	The observed infection eccentricity of node v
v ^†	The estimator of the information source
v ^∗	The actual information source
$t_{v}^{*}$	The time duration associated to the optimal sample path in which node v is the
	information source
$C (v)$	The set of children of v
ϕ(v)	The parent of node v
$Y^{k}$	The set of infection topologies where the maximum distance from the source to
	an infected node is k
T _v	The tree rooted in v
$T_{v}^{- u}$	The tree rooted in v without the branch from its neighbor u
$X ([0, t], T_{v}^{- u})$	The sample path restricted to topology $T_{v}^{- u}$
$t_{v}^{I}, t_{v}^{R}$	The infection time and recovery time of node v
d(v,u)	The length of the shortest path between node v and node u