Name
Abstract | ||
|---|---|---|
An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within $n^{\frac{1}{2}-\varepsilon}$, for any ε0, unless P=NP. If the preference lists contain ties, we improve this result to n1−ε. Also, we show that, given an integer K and an sr instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an sr instance I. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/11671411_1 | WAOA |
Keywords | Field | DocType |
roommates problem,preference list,classical stable roommates problem,integer k,stable matching,fewest number,minimum number,n agent,lower bound,sr instance,stable partition,upper and lower bounds | Integer,Stable roommates problem,Approximation algorithm,Discrete mathematics,Mathematical optimization,Combinatorics,Upper and lower bounds,Matching (graph theory),Partition (number theory),Time complexity,Mathematics,Polynomial method | Conference |
Volume | ISSN | ISBN |
3879 | 0302-9743 | 3-540-32207-8 |
Citations | PageRank | References |
22 | 1.38 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David J. Abraham | 1 | 190 | 15.88 |
| Péter Biró | 2 | 237 | 19.83 |
| David F. Manlove | 3 | 761 | 60.45 |