DMGA: A Distributed Shortest Path Algorithm for Multistage Graph

Table 1

Notation overview.

Symbol	Definition
G = (V, E, W)	Graph with vertices set , edges set , and edge weights’ set
m	Number of stages in a multistage graph
Vi	Set of vertices of stage i of a multistage graph
ni	Number of vertices of stage i of a multistage graph
	The jth vertex in the ith stage of a multistage graph
	Weight of edge <, >
Ei	Set of edges from Vi to Vi+1
ck,i,l,j	Cost of the shortest path from vertex to
CNi	The ith partition or computing node
p	Number of partitions
Cap	Capacity of each computing node
ML	Maximum load of each partition
Sum	Number of edges of a partition
sk	The first stage of CNk
ek	The last stage of CNk
	Index of the previous vertex of in the shortest path from to
	List of vertices of the shortest path from to
R	Set of partition IDs
SPLk	Set of the shortest paths storing on CNk