## 248 Citations

### Stable Marriage with Ties and Unacceptable Partners

- Economics
- 1999

An instance of the classical stable marriage problem involves n men and n women, and each person ranks all n members of the opposite sex in strict order of preference. The effect of allowing ties in…

### Stable Marriage with General Preferences - Extended Abstract

- Economics, Computer ScienceSAGT
- 2014

It is proved that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP- complete, showing this way that a natural attempt to resolve the existence (or not) of3D stable matchings is bound to fail.

### Inapproximability of Stable Marriage Problems

- Economics
- 2001

The stable marriage problem has received considerable attention both due to its practical applications as well as its mathematical structure. While the original problem has all participants rank all…

### Inapproximability Results on Stable Marriage Problems

- EconomicsLATIN
- 2002

The stable marriage problem has received considerable attention both due to its practical applications as well as its mathematical structure. While the original problem has all participants ranka ll…

### Algorithmic aspects of stable matching problems

- Mathematics
- 2007

This thesis considers stable matching problems from an algorithmic point of view, and presents both polynomial-time algorithms and NP-hardness results for a range of problems that are derived from imposing upper bounds on the length of the lists on one or both sides.

### Stability and Optimality in Matching Problems with Weighted Preferences

- EconomicsICAART
- 2011

Stable marriage problems with weighted preferences are considered: each man provides a score for each woman and it is shown that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

### Stability in Matching Problems with Weighted Preferences

- EconomicsICAART
- 2011

This work defines new notions of stability and optimality, and provides algorithms to find marriages which are stable and/or optimal according to these notions, and shows that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

## References

SHOWING 1-7 OF 7 REFERENCES

### Lower Bounds for the Stable Marriage Problem and its Variants

- Mathematics, Computer ScienceSIAM J. Comput.
- 1990

The problem of determining whether an arbitrary pair is stable in a given problem instance is studied and it is shown that the problem has a lower bound of Omega (n/sup 2/) in the worst case.

### The Stable marriage problem - structure and algorithms

- Computer ScienceFoundations of computing series
- 1989

The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a moregeneral set of problems.

### Combinatorial Optimization: Algorithms and Complexity

- Computer Science
- 1981

This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient…

### Introduction to Combinatorial Mathematics (McGraw-Hill

- New York,
- 1968