
Twosided profilebased optimality in the stable marriage problem
We study the problem of finding "fair" stable matchings in the Stable Ma...
read it

Stable divisorial gonality is in NP
Divisorial gonality and stable divisorial gonality are graph parameters,...
read it

A General Framework for Stable Roommates Problems using Answer Set Programming
The Stable Roommates problem (SR) is characterized by the preferences of...
read it

Crossidentification of stellar catalogs with multiple stars: Complexity and Resolution
In this work, I present an optimization problem which consists of assign...
read it

On Finding Maximum Cardinality Subset of Vectors with a Constraint on Normalized Squared Length of Vectors Sum
In this paper, we consider the problem of finding a maximum cardinality ...
read it

Capacity Expansion in the College Admission Problem
The college admission problem plays a fundamental role in several realw...
read it

Maximally Satisfying Lower Quotas in the Hospitals/Residents Problem with Ties
Motivated by a serious issue that hospitals in rural areas suffer from s...
read it
Profilebased optimal stable matchings in the Roommates problem
The stable roommates problem can admit multiple different stable matchings. We have different criteria for deciding which one is optimal, but computing those is often NPhard. We show that the problem of finding generous or rankmaximal stable matchings in an instance of the roommates problem with incomplete lists is NPhard even when the preference lists are at most length 3. We show that just maximising the number of first choices or minimising the number of last choices is NPhard with the short preference lists. We show that the number of R^th choices, where R is the minimumregret of a given instance of SRI, is 2approximable among all the stable matchings. Additionally, we show that the problem of finding a stable matching that maximises the number of first choices does not admit a constant time approximation algorithm and is W[1]hard with respect to the number of first choices. We implement integer programming and constraint programming formulations for the optimality criteria of SRI. We find that constraint programming outperforms integer programming and an earlier answer set programming approach by Erdam et. al. (2020) for most optimality criteria. Integer programming outperforms constraint programming and answer set programming on the almost stable roommates problem.
READ FULL TEXT
Comments
There are no comments yet.