all its neighbors and broadcast the position of $u$. In Line \[quadCountge4\], we use a variable $v.\textit{Count}$, which indicates the number of localized neighbors of $v$. Thus, if some neighbor $v$ of $u$ has at least $4$ localized neighbors, we check if it can be localized with respect to these neighbors in Line \[canBeLocalized\]. Remember that if the localized neighbors are coplanar, then we cannot fix the position of $v$. If $v$ can be localized, then we add it to $Q_{\textit{localized}}$, and continue the algorithm until the queue is empty. Finally, we return the point formation in Line \[quadReturnBest\].

**Complexity analysis.** In a network graph with $n$ vertices and $m$ edges, Algorithm \[alg:quadrialteration\] runs in $\OO(n^4m)$ time in the worst case.

Notice that even though the network graph admits a proper ordering to run the algorithm, the first $K_4$ we find in Line \[seednodes\] might not be the correct vertices to start [@theory]. As four distance measurements from four vertices in general position are sufficient to localize a node, $\OO(m)$ time is spent in each phase by using the queue data structure keeping the track of localized nodes. This can be accomplished by keeping the track of the number of 