Longest acyclic path in a directed unweighted graph

What algorithm can be used to find the longest path in an unweighted directed acyclic graph?

Dynamic programming. It is also referenced in Longest path problem, given that it is a DAG.

The following code from Wikipedia:

algorithm dag-longest-path is
    input: 
         Directed acyclic graph G
    output: 
         Length of the longest path

    length_to = array with |V(G)| elements of type int with default value 0

    for each vertex v in topOrder(G) do
        for each edge (v, w) in E(G) do
            if length_to[w] <= length_to[v] + weight(G,(v,w)) then
                length_to[w] = length_to[v] + weight(G, (v,w))

    return max(length_to[v] for v in V(G))

As long as the graph is acyclic, all you need to do is negate the edge weights and run any shortest-path algorithm.

EDIT: Obviously, you need a shortest-path algorithm that supports negative weights. Also, the algorithm from Wikipedia seems to have better time complexity, but I'll leave my answer here for reference.

Wikipedia has an algorithm: http://en.wikipedia.org/wiki/Longest_path_problem

Looks like they use weightings, but should work with weightings all set to 1.

Can be solved by critical path method:
1. find a topological ordering
2. find the critical path
see [Horowitz 1995], Fundamentals of Data Structures in C++, Computer Science Press, New York.

Greedy strategy(e.g. Dijkstra) will not work, no matter:1. use "max" instead of "min" 2. convert positive weights to negative 3. give a very large number M and use M-w as weight.