Source code online books for professionals by professionals

Set and vertex covers. A vertex cover is a set of vertices that cover (that is, are adjacent to) all the edges of the graph. 
A set cover is a generalization of this idea, where the nodes are replaced with subsets, and you want to cover the entire 
set. The problem lies in constraining or minimizing the number of nodes/subsets. Both problems are NP-hard  
(see Chapter 11).
Shortest paths. This problem involves finding the shortest path from one node to another, from one node to all the 
others (or vice versa), or from all nodes to all others. The one-to-one, one-to-all, and all-to-one cases are solved 
the same way, normally using BFS for unweighted graphs, DAG shortest path for DAGs, Dijkstra’s algorithm for 
nonnegative edge weights, and Bellman–Ford in the general case. To speed up things in practice (although without 
affecting the worst-case running time), you can also use bidirectional Dijkstra, or the A* algorithm. For the all pairs 
shortest paths problem, the algorithms of choice are probably Floyd–Warshall or (for sparse graphs) Johnson’s 
algorithm. If the edges are nonnegative, Johnson’s algorithm is (asymptotically) equivalent to running Dijkstra’s 
algorithm from every node (which may be more effective). (For more information on shortest path algorithms, see 
Chapters 5 and 9.) Note that the longest path problem (for general graphs) can be used to find Hamilton paths, which 
means that it is NP-hard. This, in fact, means that the shortest path problem is also NP-hard in the general case. If we 
disallow negative cycles in the graph, however, our polynomial algorithms will work.