Question

I have a random undirected social graph.

I want to find a Hamiltonian path if possible. Or if not possible (or not possible to know if possible in polynomial time) a series of paths. In this “series of paths” (where all N nodes are used exactly once), I want to minimize the number of paths and maximize the average length of the paths. (So no trivial solution of N paths of a single node).

I have generated an adjacency matrix for the nodes and edges already.

Any suggestions? Pointers in the right direction? I realize this will require heuristics because of the NP-complete (?) nature of the problem, and I am OK with a “good enough” answer. Also I would like to do this in Java.

Thanks!

Answer 1

Use a genetic algorithm (without crossover), where each individual is a permutation of the nodes. This gives you “series of paths” at each generation, evolving to a minimal number of paths (1) and a maximal avg. length (N).