Shortest Path Problems
•Directed weighted graph.
•Path length is sum of weights of edges on path.
•The vertex at which the path begins is the
source vertex.
•The vertex at which the path ends is the
destination vertex.
Example
A path from 1to 7.
1
2
3
4
5
6
7
2
616 7
8
10
3
14
44
5 3
1
1
7
Path length is 14.
Example
Another path from 1to 7.
1
2
3
4
5
6
7
2
616 7
8
10
3
14
44
5 3
1
Path length is 11.
Shortest Path Problems
•Single source single destination.
•Single source all destinations.
•All pairs (every vertex is a source
and destination).
Single Source Single Destination
Possible greedy algorithm:
Leave source vertex using cheapest/shortest edge.
Leave new vertex using cheapest edge subject to the
constraint that a new vertex is reached.
Continue until destination is reached.
Greedy Shortest 1 To 7 Path
1
2
3
4
5
6
7
2
616 7
8
10
3
14
44
5 3
1
Path length is 12.
Not shortest path. Algorithm doesn’t work!
