Finding robust solutions to stable marriage

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a,b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1,b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1,b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches

A one-shot deviation principle for stability in matching problems

This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation

A one-shot deviation principle for stability in matching problems

This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation

A one-shot deviation principle for stability in matching problems

This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation

On the complexity of Robust Stable Marriage

Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We focus on the complexity of finding an (a, b)-supermatch. An (a, b)-supermatch is defined as a stable matching in which if any a (non-fixed) men/women break up it is possible to find another stable matching by changing the partners of those a men/women and also the partners of at most b other couples. In order to show deciding if there exists an (a, b)-supermatch is NPNP -complete, we first introduce a SAT formulation that is NPNP -complete by using Schaefer’s Dichotomy Theorem. Then, we show the equivalence between the SAT formulation and finding a (1, 1)-supermatch on a specific family of instances

Economic Trajectories in Non-Traditional Families with Children

Using data from the Fragile Families and Child Wellbeing Study this paper examines associations between family structure and economic trajectories during the first five years after a child’s birth, paying special attention to non-traditional families. Among families with stable structures, married-parent families have the highest economic wellbeing, followed by cohabiting-parent families and then single mothers. Among unstable families, exits from marriage and cohabitation are associated with declines in mothers’ economic wellbeing. Entering coresidential unions after a non-marital birth is associated with gains in single mothers’ economic wellbeing, especially if those unions involve the child’s biological father. Findings are robust across several measures of economic wellbeing including household income, income-to-needs ratios, and material hardship.family structure, divorce, cohabitation, income, Fragile Families and Child Wellbeing Study (FFCWS), growth curve analysis

Changing patterns of religious affiliation, church attendance and marriage across five areas of Europe since the early 1980s: trends and associations

This study draws on three waves of the European Values Survey (conducted between 1981 and 1984, between 1989 and 1993, and between 1999 and 2004) across five countries for which full data are available (Great Britain, Italy, the Netherlands, Northern Ireland, Spain, and Sweden) in order to address five research questions. Question one examined changes in religious affiliation. Across all five countries, the proportions of the non-affiliated increased. Question two examined changes in church attendance. Across all five countries, the proportions of the non-attenders increased. Question three examined changes in marital status. Across all five countries the proportions of the population checking the category 'married' declined, although in Spain the decline was marginal. Question four examined the association between religious affiliation and being married. The religious affiliated were more likely to be married than the non-affiliated. Question five examined the association between church attendance and being married. Weekly attenders were more likely to be married than the non-attenders. Overall these data support the close association between religion and marriage across five European countries (where there are very different religious climates) and support the hypothesis that changing religious values and changing family values go hand-in-hand