Algorithm 1k-hop greedy routing.

Function greedy-routing (s, $\mathcal{F}$, k);  Input: A target slice (s), a set of flows ($\mathcal{F}$), number of interference hops (k)  Output: A routing matrix of slice s, which is a zero-matrix if the routing fails  1:if$s=1$then  2: $R\leftarrow$ shortest-path ($G_1$, $\mathcal{F}$)  3: if R does not satisfy the constraints in Equations (7) and (8) then  4:  return ${\{0\}}_{|\mathcal{F}|\times |{\mathcal{E}}_1|}$ // zero-matrix  5: end if  6:else  7: $R\leftarrow$${\{0\}}_{|\mathcal{F}|\times |{\mathcal{E}}_s|}$ // initialize  8: Calculate $c_s^k(e)$ for $\forall e\in {\mathcal{E}}_s$ using (14)  9: while $\mathcal{F}\ne \varnothing$ do 10:  $f\leftarrow$ a flow with the highest rate among all flows of $\mathcal{F}$ 11:  ${\mathcal{P}}_{f,s}\leftarrow$ a path minimizing ${\sigma }_s^k$ while satisfying the constraints in Equations (7) and (8) under the given matrix R 12:  if no feasible ${\mathcal{P}}_{f,s}$ then 13:   return ${\{0\}}_{|\mathcal{F}|\times |{\mathcal{E}}_s|}$ 14:  end if 15:  Update R with ${\mathcal{P}}_{f,s}$ 16:  $\mathcal{F}\leftarrow \mathcal{F}-\{f\}$ 17: end while 18:end if 19:$R_s\leftarrow R$ // update the routing matrix of slice s 20:Route flows of slice s using the updated matrix $R_s$ 21:return$R_s$ // the updated routing matrix of slice s