Hamiltonian path problem

The Hamiltonian cycle problem is a special case of the travelling salesman problem, obtained by setting the distance between two cities to one if they are adjacent and two otherwise, and verifying that the total distance travelled is equal to n. If so, the route is a Hamiltonian cycle.

The algorithm also divides the graph into components that can be solved separately, greatly reducing the search size.

Also, a dynamic programming algorithm of Bellman, Held, and Karp can be used to solve the problem in time O(n2 2n).

[8] For graphs of maximum degree three, a careful backtracking search can find a Hamiltonian cycle (if one exists) in time O(1.251n).

For instance, Leonard Adleman showed that the Hamiltonian path problem may be solved using a DNA computer.

[11] The idea is to create a graph-like structure made from optical cables and beam splitters which are traversed by light in order to construct a solution for the problem.

The weak point of this approach is the required amount of energy which is exponential in the number of nodes.

[21] The Hamiltonian path problem is NP-Complete meaning a proposed solution can be verified in polynomial time.

[22] Networks on chip (NoC) are used in computer systems and processors serving as communication for on-chip components.

Utilizing this strategy guarantees deadlock and livelock free routing, increasing the efficiency of the NoC.

[26] Rendering engines are a form of software used in computer graphics to generate images or models from input data.