I need to select a given number of nodes from a weighted directed graph such that the nodes selected are the closest to a given starting node. This seems like a common problem to need to solve, but I haven't found much material on it. Does anyone know if this particular problem has a name, or any published material (formal or informal) related to it?
Note, I am not asking for a solution to the problem itself. I am interested in finding material related to the problem. For very large graphs, the canonical Dijkstra algorithm will not work because you must enqueue every node first. I believe a modified version of the Uniform Cost Search will do what I want, since it does not enqueue all the nodes first. Things get more interesting in this case, because you don't have full knowledge of all shortest paths. I'm interested in things like how do you know when you've found all the shortest paths for the closest nodes, without traversing the entire graph in the process. I think this is possible using an admissible heuristic as in the A* search. These are the kinds of details I want to be able to read up on.