The Generalized Stable Allocation Problem

We introduce and study the generalized stable allocation problem, an “ordinal” variant of the well-studied generalized assignment problem in which we seek a fractional assignment that is stable (in the same sense as in the classical stable marriage problem) with respect to a two-sided set of ranked preference lists. We develop an O(m logn) algorithm for solving this problem in a bipartite assignment graph with n nodes and m edges. When edge costs are present, we show that it is NP-hard to compute a stable assignment of minimum cost, a result that stands in stark contrast with most other stable matching problems (e.g., the stable marriage and stable allocation problems) for which we can efficiently optimize over the set of all stable assignments.