dijkstra's algorithm (note* there are different kinds of dijkstra's implementation) and growth graph algorithm

Dijkstra's algorithm is used by the OSPF and the IS-IS routing protocols. The last three letters in OSPF (SPF) mean "shortest path first", which is an alternative name for Dijkstra's algorithm.

Dijkstra's original algorithm (published in 1959) has a time-complexity of O(N*N), where N is the number of nodes.

Dijkstra's algorithm has importance when you are trying to find the shortest path between two points. It's used in the computer networking field where routing protocols, like OSPF, uses it to find the shortest path between routers.

http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

No, Dijkstra's algorithm can not be used when there are negative arc lengths.

In Dijkstra's, the vertex that can be reached from the current set of labeled vertices and that of having the minimum weight among the alternatives is permanently labeled in that iteration. Since a negative arc weight would result in changing the label of a pre-permanently-labeled vertex, the algo collapses.

Bellman's algorithm is used with negative arc lengths.