Directed Acyclic Graph Traversal in Java Web Application

Question

So I am building a web application where you can build a directed graph where a node will represent some operation and the edge will represent data flow between those operations. So for an edge {u,v} , u must run before v does. Click this link to see a sample graph

START node represents the initial value and the other nodes except the output does the operation as specified. Output node will output the value it receives as input.

Which algorithm approach should i use to process a graph like that ?

Answer 1

This is a perfect example of a topological sort. The most common algorithm for creating a set following the order requirements via traversing is Kahn's Algorithm. The pseudocode can be seen below and the information in the Wikipedia link should be enough to get you started.

L ← Empty list that will contain the sorted elements
S ← Set of all nodes with no incoming edges
while S is non-empty do
    remove a node n from S
    add n to tail of L
    for each node m with an edge e from n to m do
        remove edge e from the graph
        if m has no other incoming edges then
            insert m into S
if graph has edges then
    return error (graph has at least one cycle)
else 
    return L (a topologically sorted order)

Note the "starting node" will be enforced by properly representing the incoming edges in the graph. It will be the only node in S to start. Please let me know in the comments if you would like any other information.