Solutions for the stable roommates problem with payments

Abstract

The stable roommates problem with payments has as input a graph G∈=∈(V,E) with an edge weighting w: E∈→∈ ∈+∈ and the problem is to find a stable solution. A solution is a matching M with a vector that satisfies p u ∈+∈p v ∈=∈w(uv) for all uv∈ ∈M and p u ∈=∈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 p u ∈+∈p v ∈