Noon-Bean Transformation

Noon-Bean Transformation to transform a GTSP instance to an ATSP instance

The function is an implementation of the Noon-Bean Transformation to transform an instance of the Generalized Travelling Salesman Problem (GTSP) to an equivalent instance of the Asymmetric Travelling Salesman Problem (ATSP).

Definitions:
GTSP: Consider a graph with its vertices partitioned into mutually exclusive vertex sets. Find the shortest path that visits one vertex in each set.

The Noon Bean Transformation convert a GTSP instance into a ATSP instance such that the optimal solution to the ATSP can be used to extract the optimal solution to the GTSP.

Inputs:
1. Full adjacency matrix for the GTSP
2. Set Mapping

Outputs:
1. ATSP adjacency matrix