processors. Our algorithm is build for the situations where the number of processing cores is large but not at the same scale as the number of vertices. On the other hand our algorithm may not be effective for the wireless networks since the underlying graph structure does not imply that the vertices are of bounded degree.

The execution time of the algorithm is influenced by the sizes of the sets of active vertices, active edges, and phantom edges. The cardinalitiles of these sets are order of magnitude smaller than the size of the graph. Although this cannot be proved at the moment, we will provide a justification on how existing conjectures and theorems from the percolation theory provide some estimates on the sizes of these sets. The set of active vertices is related to the limit shape in the model of first passage percolation introduced by Hammersley and Welsh [@hammersley_welsh]. The first passage percolation corresponds to the case $M=\infty$, i.e. the case when there are no constraints. If we assume that $A=\{0\}$, for each time $t$ we can define the ball of radius $t$ in the first passage percolation metric as: $$B_t=\left\{x: \tau(0,x)\leq t\right\},$$ where $\tau(0,x)$ is the [*first passage 