Solutions for the stable roommates problem with payments

The stable roommates problem with payments has as input a graph G=(V,E) with an edge weighting w:E→R≥0 and the problem is to find a stable solution. A solution is a matching M with a vector that satisfies pu+pv=w(uv) for all uv∈M and pu=0 for all u unmatched in M. A solution is stable if it prevents blocking pairs, i.e., pairs of adjacent vertices u and v with pu+pv