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 Stable Marriage Requires Communication

The Gale-Shapley algorithm for the Stable Marriage Problem is known to take $\Theta(n^2)$ steps to find a stable marriage in the worst case, but only $\Theta(n \log n)$ steps in the average case (with $n$ women and $n$ men). In 1976, Knuth asked whether the worst-case running time can be improved in a model of computation that does not require sequential access to the whole input. A partial negative answer was given by Ng and Hirschberg, who showed that $\Theta(n^2)$ queries are required in a model that allows certain natural random-access queries to the participants' preferences. A significantly more general - albeit slightly weaker - lower bound follows from Segal's general analysis of communication complexity, namely that $\Omega(n^2)$ Boolean queries are required in order to find a stable marriage, regardless of the set of allowed Boolean queries. Using a reduction to the communication complexity of the disjointness problem, we give a far simpler, yet significantly more powerful argument showing that $\Omega(n^2)$ Boolean queries of any type are indeed required for finding a stable - or even an approximately stable - marriage. Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, (C) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage, and (D) determining whether a proposed marriage is stable or far from stable. In order to analyze "approximately stable" marriages, we introduce the notion of "distance to stability" and provide an efficient algorithm for its computation

Partial Identification in Matching Models for the Marriage Market

We study partial identification of the preference parameters in models of one-to-one matching with perfectly transferable utilities, without imposing parametric distributional restrictions on the unobserved heterogeneity and with data on one large market. We provide a tractable characterisation of the identified set, under various classes of nonparametric distributional assumptions on the unobserved heterogeneity. Using our methodology, we re-examine some of the relevant questions in the empirical literature on the marriage market which have been previously studied under the Multinomial Logit assumption

Constraints, Lazy Constraints, or Propagators in ASP Solving: An Empirical Analysis

Answer Set Programming (ASP) is a well-established declarative paradigm. One of the successes of ASP is the availability of efficient systems. State-of-the-art systems are based on the ground+solve approach. In some applications this approach is infeasible because the grounding of one or few constraints is expensive. In this paper, we systematically compare alternative strategies to avoid the instantiation of problematic constraints, that are based on custom extensions of the solver. Results on real and synthetic benchmarks highlight some strengths and weaknesses of the different strategies. (Under consideration for acceptance in TPLP, ICLP 2017 Special Issue.)Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017. 16 page

Unveiling Hidden Values of Optimization Models with Metaheuristic Approach

Considering that the decision making process for constrained optimization problem is based on modeling, there is always room for alternative solutions because there is usually a gap between the model and the real problem it depicts. This study looks into the problem of finding such alternative solutions, the non-optimal solutions of interest for constrained optimization models, the SoI problem. SoI problems subsume finding feasible solutions of interest (FoIs) and infeasible solutions of interest (IoIs). In all cases, the interest addressed is post-solution analysis in one form or another. Post-solution analysis of a constrained optimization model occurs after the model has been solved and a good or optimal solution for it has been found. At this point, sensitivity analysis and other questions of import for decision making come into play and for this purpose the SoIs can be very valuable. An evolutionary computation approach (in particular, a population-based metaheuristic) is proposed for solving the SoI problem and a systematic approach with a feasible-infeasible- two-population genetic algorithm is demonstrated. In this study, the effectiveness of the proposed approach on finding SoIs is demonstrated with generalized assignment problems and generalized quadratic assignment problems. Also, the applications of the proposed approach on the multi-objective optimization and robust-optimization issues are examined and illustrated with two-sided matching problems and flowshop scheduling problems respectively

The Empirical Turn In Family Law

Historically, the legal system justified family law’s rules and policies through morality, common sense, and prevailing cultural norms. In a sharp departure, and consistent with a broader trend across the legal system, empirical evidence increasingly dominates the regulation of families. There is much to celebrate in this empirical turn. Properly used, empirical evidence in family law can help the state act more effectively and efficiently, unmask prejudice, and depoliticize contentious battles. But the empirical turn also presents substantial concerns. Beyond perennial issues of the quality of empirical evidence and the ability of legal actors to use it, there are more fundamental problems: Using empirical evidence focuses attention on the outcomes of legal rules, discouraging a debate about contested and competing values. Reliance on empirical evidence overlays a veneer of neutrality on normative judgments. And uncritically adopting evidence about present conditions without interrogating the role of historical discrimination that continues to disadvantage some families can replicate that discrimination. Given the promise and peril of the empirical turn in family law, this Essay proposes a framework to guide the use of this evidence. The framework preserves space for debating multiple values and advises decisionmakers when to use empirical evidence, with particular attention to the dangers for nondominant families. The framework also recommends strengthening evidentiary gatekeeping and elevating the potential for legal scholarship to serve as a bridge from the broader research base to the courts. With this guidance in place, empirical evidence can take its rightful place as a useful but cabined tool in the legal regulation of families