Finding the Shortest Path with Vertex Constraint over Large Graphs

Algorithm 2

APPROXIMATE-PATH ().

Input:.

Output:.

// Input: : an undirected weighted graph

// : a vertex subset of

// , : starting vertex and ending vertex respectively

// Output: : the approximate shortest path between and

// with vertexconstraint of

1: Let be a min priority queue with the entries in the form , sorted in the ascending order of

, where is the shortest distance between and ;

2: ;

3: for  each    do

4: Enqueue an entry into ;

5: , ;

6: while    do

7: Dequeue the first entry from ;

8: if    then

9: continue;

10: else

11: , ;

12: for  each    do

13: Enqueue an entry into ;

14: ;

15: Traverse by preorder and let be a permutation corresponding to the order of

vertices in preorder traversal on ;

16: Move the ending vertex to the end of to get ;

17: Generate the shortest path between and under a permutation ;

18: return  ;