What is the problem name for Traveling salesman problem(TSP) without considering going back to starting point?

Question

I would like to know what is the problem name for TSP w/o considering the way of going back to starting point and what is the algorithm to solve this.

I looked into

Answer 1

If I understand correctly, you want to find the shortest path (that starts from some vertex s) and goes through all the nodes in the graph without visiting the same node twice. A simpler problem, is the hamiltonian path problem. It asks, like you said, weather there exists such a path or not. Since that problem is NP-hard, and it's easier than your problem, solving your problem is at least NP-Hard. Well, that isn't true because your problem is not a decision problem. But what it does say is that we can almost be sure that there is no polynomial algorithm for your problem.

You can resort to approximation. There is a pretty cool approximation for the metric TSP here: http://en.wikipedia.org/wiki/Travelling_salesman_problem#Metric_TSP.