Article ID: | iaor2004777 |
Country: | United States |
Volume: | 27 |
Issue: | 3 |
Start Page Number: | 485 |
End Page Number: | 503 |
Publication Date: | Aug 2002 |
Journal: | Mathematics of Operations Research |
Authors: | Baou Mourad, Balinski Michel |
The stable allocation problem generalized the 0,1 stable matching problems (one-to-one, one-to-many, and many-to-many) to the allocation of real valued hours or quantities. A strongly polynomial algorithm proves the existence of ‘stable allocations’. The set of stable allocations is shown to be a distributive lattice in general, but in the ‘nondegenerate’ case it is a complete linear order. Indeed, in the generic case, when a problem is ‘strongly nondegenerate’, there exists a single stable allocation. A simple algorithm finds ‘row-optimal’ and ‘column-optimal’ stable allocations, given any stable allocation. When a problem is nondegenerate it finds all stable allocations.