Algorithm 1 Given two clusters and an observation point, check whether the clusters are collision free.
1:	CollidingClusters( ${\mathcal{LC}}_i$, ${\mathcal{LC}}_{i-\mathit{1}}$, Oi)
2:	for $\tau \in {\mathcal{T}}^i\cup {\mathcal{T}}^{i–1}$ do
3:	if ϕ(τ, Oi, t) < 0 then
4:	return FALSE.
5:	if $B_i\cap B_{i-1}^{\prime }\ne \mathit{NULL}$ then
6:	return FALSE.
7:	return TRUE.