Algorithm 1. Registration of Candidate for Server Placement of a Certain Service
1	Input:
2	$v\leftarrow$ an input service
3	$\mathcal{N}\leftarrow$ the set of edge nodes
4	$\mathcal{C}\leftarrow$$\mathrm{the} \mathrm{set} \mathrm{of} \mathrm{clients} \mathrm{using} \mathrm{the} \mathrm{service} v$
5
6	$\mathbb{C}\leftarrow$$\mathrm{set} \mathrm{as} \mathrm{empty} \mathrm{list} \mathrm{for} \mathrm{the} \mathrm{server} \mathrm{placement} \mathrm{candidates} \mathrm{for} \mathrm{service} v$
7	for$\lambda \leftarrow \left[1,\min \left(\left|\mathcal{N}\right|,\left|\mathcal{C}\right|\right)\right]$do
8	$S_{\lambda }\leftarrow$$\mathrm{the} \mathrm{set} \mathrm{of} \mathrm{servers} \mathrm{when} \mathrm{service} v$$\mathrm{has} \lambda$ of servers
9	$A_{\lambda }\leftarrow GetServerAssignment\left(\mathcal{N},S_{\lambda }\right)$
10	// The set of assignments for $\lambda$ of servers $A_{\lambda }$ consists of sets of key-value pairs
11	// key: a server, value: a node running the server
12	// i.e., $A_{\lambda }=\left\{\left\{s_1:n_5,s_2:n_7,s_3:n_2,\dots \right\}, \left\{\dots \right\}, \dots \right\}, \forall s_i\in S_{\lambda },\forall n_j\in \mathcal{N}$
13	for each $a\in A_{\lambda }$ do
14	${\tau }_a^{sync}\leftarrow GetSyncTraffic\left(v, a\right)$
15	$M_a\leftarrow GetMappingInfo\left(\mathcal{C}, a\right)$
16	// The set of mapping information for assignment $a$, $M_a$ consists of sets of key-value pairs
17	// key: a client, value: a server mapped with the client
18	// i.e., $M_a=\left\{\left\{c_1:s_2,c_2:s_2,c_3:s_1,\dots \right\}, \left\{\dots \right\}, \dots \right\},\forall c_i\in \mathcal{C}, \forall s_j\in S_{\lambda }$
19	for each $m\in M_a$ do
20	$r_m^{base}\leftarrow GetBaseResource\left(v\right)$
21	${\tau }_m\leftarrow {\tau }_a^{sync}$
22	for each $c\in m.Keys$ do
23	$s_c\leftarrow$ the server mapped with client $c$
24	${\tau }_m\leftarrow {\tau }_m+u_c\times f_t^v\times dist\left(s_c, c\right)$
25	$r_m^{s_c}\leftarrow r_m^{s_c}+u_c\times \left[f_{cpu}^v, f_{mem}^v, f_{sto}^v\right]$
26	end for
27	for each $s\in S_{\lambda }$ do
28	$r_m^s\leftarrow r_m^{base}+r_m^s$
29	$R_m.Add\left(r_m^s\right)$
30	end for
31	${\mathrm{𝕔}}_{\lambda }^m\leftarrow CreateCandidate\left(a,m, {\tau }_m,R_m\right)$
32	$\mathbb{C}.Register\left({\mathrm{𝕔}}_{\lambda }^m\right)$
33	end for
34	end for
35	$\mathbb{C}.Sort\left(\tau ,ascending\right)$
36	if $\lambda >1 \wedge \nexists {\mathrm{𝕔}}_{\lambda }^m\in \mathbb{C}, {\mathrm{𝕔}}_{\lambda }^m.\tau <{\mathrm{𝕔}}_{\lambda -1}^m.\tau$ then break
37	end for
38
39	Output:
40	return$\mathbb{C}$