Local search for stable marriage problems with ties and incomplete lists

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. This problem is NP-hard. We tackle this problem using local search, exploiting properties of the problem to reduce the size of the neighborhood and to make local moves efficiently. Experimental results show that this approach is able to solve large problems, quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun eds., Springer LNA

Stable marriage with general preferences

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable marriage where preferences are allowed to have ties and to be incomplete. As a result, we prove that deciding the existence of a stable matching in our model is NP-complete. Complementing this negative result we present a polynomial-time algorithm for the above decision problem in a significant class of instances where the preferences are asymmetric. We also present a linear programming formulation whose feasibility fully characterizes the existence of stable matchings in this special case. Finally, we use our model to study a long standing open problem regarding the existence of cyclic 3D stable matchings. In particular, we prove 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) of 3D stable matchings is bound to fail.Comment: This is an extended version of a paper to appear at the The 7th International Symposium on Algorithmic Game Theory (SAGT 2014

Popular matchings in the marriage and roommates problems

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8

Climate change, hazards and vulnerability: multiscale analysis in northern coast of São Paulo, Brazil.

This study focus into two different approaches to assess hazards and vulnerabilities: (1) the geospatial indicators and (2) modelling of debris flow and flooding events. The integration of both methods through a multiscale analysis: (i) in a regional scale, geospatial indicators show the priority watersheds for risk reduction in the different hazards - landslides, flooding and rising sea level, (ii) locally, the analysis based on a 1967s extreme event in Caraguatatuba - with rainfall variation of 115-420mm and max. 841mm - show the consistent analysis of historical data of tidal levels and the rainfall effects of flooding and debris flow in the districts of ?Santo Antônio' river basin

Vascular Complications of Pancreatitis: Role of Interventional Therapy

Major vascular complications related to pancreatitis can cause life-threatening hemorrhage and have to be dealt with as an emergency, utilizing a multidisciplinary approach of angiography, endoscopy or surgery. These may occur secondary to direct vascular injuries, which result in the formation of splanchnic pseudoaneurysms, gastrointestinal etiologies such as peptic ulcer disease and gastroesophageal varices, and post-operative bleeding related to pancreatic surgery. In this review article, we discuss the pathophysiologic mechanisms, diagnostic modalities, and treatment of pancreatic vascular complications, with a focus on the role of minimally-invasive interventional therapies such as angioembolization, endovascular stenting, and ultrasound-guided percutaneous thrombin injection in their management

Bmi1 Confers Resistance to Oxidative Stress on Hematopoietic Stem Cells

The polycomb-group (PcG) proteins function as general regulators of stem cells. We previously reported that retrovirus-mediated overexpression of Bmi1, a gene encoding a core component of polycomb repressive complex (PRC) 1, maintained self-renewing hematopoietic stem cells (HSCs) during long-term culture. However, the effects of overexpression of Bmi1 on HSCs in vivo remained to be precisely addressed.In this study, we generated a mouse line where Bmi1 can be conditionally overexpressed under the control of the endogenous Rosa26 promoter in a hematopoietic cell-specific fashion (Tie2-Cre;R26Stop(FL)Bmi1). Although overexpression of Bmi1 did not significantly affect steady state hematopoiesis, it promoted expansion of functional HSCs during ex vivo culture and efficiently protected HSCs against loss of self-renewal capacity during serial transplantation. Overexpression of Bmi1 had no effect on DNA damage response triggered by ionizing radiation. In contrast, Tie2-Cre;R26Stop(FL)Bmi1 HSCs under oxidative stress maintained a multipotent state and generally tolerated oxidative stress better than the control. Unexpectedly, overexpression of Bmi1 had no impact on the level of intracellular reactive oxygen species (ROS).Our findings demonstrate that overexpression of Bmi1 confers resistance to stresses, particularly oxidative stress, onto HSCs. This thereby enhances their regenerative capacity and suggests that Bmi1 is located downstream of ROS signaling and negatively regulated by it

Severe airway stenosis associated with Crohn's disease: Case report

BACKGROUND: Symptomatic respiratory tract involvement is not common in Crohn's disease. Upper-airway obstruction has been reported before in Crohn's disease and usually responds well to steroid treatment. CASE PRESENTATION: We report a case of a 32-year old patient with Crohn's disease who presented with progressively worsening dyspnea on exertion. Magnetic Resonance Imaging of the chest and bronchoscopy revealed severe tracheal stenosis and marked inflammation of tracheal mucosa. Histopathology of the lesion showed acute and chronic inflammation and extended ulceration of bronchial mucosa, without granulomas. Tracheal stenosis was attributed to Crohn's disease after exclusion of other possible causes and oral and inhaled steroids were administered. Despite steroid treatment, tracheal stenosis persisted and only mild symptomatic improvement was noted after 8 months of therapy. The patient subsequently underwent rigid bronchoscopy with successful dilatation and ablation of the stenosed areas and remission of her symptoms. CONCLUSION: Respiratory involvement in Crohn's disease might be more common than appreciated. Interventional pulmonology techniques should be considered in cases of tracheal stenosis due to Crohn's disease refractory to steroid treatment