That problem, which is not known to be in either P and NP-complete, is to find whether an isomorphism exists between two of these structures.
Cole and Vishkin gave a distributed algorithm which runs on one of these objects in "log star" of n time. An algorithm which works on them assigns all values in a string to infinity except the source and then relaxes repeatedly. Laszlo Babai recently claimed to have an algorithm which solves a problem about these structures in quasi-polynomial time. That problem, which is not known to be in either P and NP-complete, is to find whether an isomorphism exists between two of these structures. Iterative deepening improves efficiency when (*) searching these objects, and bipartite ones may be colored with two colors. A greedy algorithm which works on these objects by always choosing the lowest weight is called Dijkstra's algorithm and finds a minimum path on them. These objects may be represented by an adjacency tree or list. For 10 points, name these directed or undirected constructs which consist of a bunch of vertices connected by a bunch of edges
Cole and Vishkin gave a distributed algorithm which runs on one of these objects in "log star" of n time.
graphs [accept trees] 