Modeling Stable Matching Problems with Answer Set Programming

The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications. Each time a new variant is considered, however, a new algorithm needs to be developed and implemented. As an alternative, in this paper we propose an encoding of the SMP using Answer Set Programming (ASP). Our encoding can easily be extended and adapted to the needs of specific applications. As an illustration we show how stable matchings can be found when individuals may designate unacceptable partners and ties between preferences are allowed. Subsequently, we show how our ASP based encoding naturally allows us to select specific stable matchings which are optimal according to a given criterion. Each time, we can rely on generic and efficient off-the-shelf answer set solvers to find (optimal) stable matchings.Comment: 26 page

The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

"Almost stable" matchings in the Roommates problem

An instance of the classical Stable Roommates problem (SR) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an SR instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within n^{\frac{1}{2}-\varepsilon}, for any \varepsilon>0, unless P=NP. If the preference lists contain ties, we improve this result to n^{1-\varepsilon}. Also, we show that, given an integer K and an SR instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an SR instance I

'The body is a battleground for unwanted and unexpressed emotions': exploring eating disorders and the role of emotional intelligence.

Emotional difficulties have been observed in individuals with eating disorders across awide range of studies, including poor interoceptive awareness, confusion of emotionalstates and difficulties with emotional language. Literature has linked these difficultieswith emotional functioning as being an important factor related to the core aetiology ofeating disorders, however limited knowledge exists to how this impacts on professionalability to engage patients within treatment as a result of such dysfunction. Using aqualitative design this paper explores how facets of Emotional intelligence (EI) arerelated to the experience of an eating disorder. The study sampled a total of 32participants with either a professional background working with eating disorders (n=25)or participants with personal lived experience (n=5), with a number of the participants(n=13) identified as having dual roles. The findings of the study show that aspects of EIsuch as emotional regulation and lack of an emotional language are considered to beat the core of the onset and maintenance of these disorders. Additional aspects ofemotional awareness and expression were found to be related to treatmentdisengagement and difficulties. Building on previous literature, this paper found suchemotional deficits as a transdiagnostic issue rather than specifically anorexia nervosa.Furthermore, such dysfunction was seen by professionals to have a considerableimpact on therapeutic relationships and successful treatment. These findings provideinsight into the potential applications that EI may have in addressing aspects of theeating disorder to create better outcomes for treatment and intervention models

Identification of a lineage of multipotent hematopoietic progenitors

All multipotent hematopoietic progenitors in C57BL-Thy-1.1 bone marrow are divided among three subpopulations of Thy-1.1^(lo) Sca-1^+ Lin^(-/lo) c-kit^+ cells: long-term reconstituting Mac-1^-CD4^-c-kit^+ cells and transiently reconstituting Mac-1^(lo)CD4^-or Mac-1^(lo) CD4^(lo) cells. This study shows that the same populations, with similar functional activities, exist in mice whose hematopoietic systems were reconstituted by hematopoietic stem cells after lethal irradiation. We demonstrate that these populations form a lineage of multipotent progenitors from long-term self-renewing stem cells to the most mature multipotent progenitor population. In reconstituted mice, Mac-1- CD4^-c-kit^+ cells gave rise to Mac-1^(lo)CD4^- cells, which gave rise to Mac-1^(lo)CD4^(lo) cells. Mac-1^- CD4^-c-kit^+ cells had long-term self-renewal potential, with each cell being capable of giving rise to more than 10^4 functionally similar Mac-1^-CD4^-c-kit^+ cells. At least half of Mac-1^(lo)CD4^- cells had transient self-renewal potential, detected in the spleen 7 days after reconstitution. Mac-1^(lo)CD4^(lo) cells did not have detectable self-renewal potential. The identification of a lineage of multipotent progenitors provides an important tool for identifying genes that regulate self-renewal and lineage commitment

Socially stable matchings in the hospitals / residents problem

In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. Such a situation is undesirable as it could lead to a deviation in which the blocking pair form a private arrangement outside the matching. This however assumes that the blocking pair have social ties or communication channels to facilitate the deviation. Relaxing the stability definition to take account of the potential lack of social ties between agents can yield larger stable matchings. In this paper, we define the Hospitals/Residents problem under Social Stability (HRSS) which takes into account social ties between agents by introducing a social network graph to the HR problem. Edges in the social network graph correspond to resident-hospital pairs in the HR instance that know one another. Pairs that do not have corresponding edges in the social network graph can belong to a matching M but they can never block M. Relative to a relaxed stability definition for HRSS, called social stability, we show that socially stable matchings can have different sizes and the problem of finding a maximum socially stable matching is NP-hard, though approximable within 3/2. Furthermore we give polynomial time algorithms for three special cases of the problem

Counting Popular Matchings in House Allocation Problems

We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the preference lists are strictly ordered. We first consider the case of ties in preference lists. Nasre proved that the problem of counting the number of popular matching is #P-hard when there are ties. We give an FPRAS for this problem. We then consider the popular matching problem where preference lists are strictly ordered but each house has a capacity associated with it. We give a switching graph characterization of popular matchings in this case. Such characterizations were studied earlier for the case of strictly ordered preference lists (McDermid and Irving) and for preference lists with ties (Nasre). We use our characterization to prove that counting popular matchings in capacitated case is #P-hard

Preliminary Results on Chemical Thinning of Apple Blossoms with Ammonium Thiosulphate, NAA, and Ethephon

Preliminary tests were carried out using ammonium thiosulphate as a chemical thinning agent for apple ('Cox's Orange Pippin' and 'Braeburn') blossoms. Ethephon and NAA (1-napthylacetic acid) were included for comparison. Whole tree sprays of 37g/l ammonium thiosulphate over-thinned 'Cox's Orange Pippin' blossoms and severely scorched blossoms, foliage, and apical meristems. Ethephon at 0.35 g/l also over-thinned, and NAA thinned to an intermediate extent when compared with the controls. When the lower concentration of 3.7 g/l ammonium thiosulphate was directly applied to stamens and styles of 'Braeburn' blossoms by brush, initial fruit set was only 30% that of untreated blossoms. When 0.35 g/I ethephon was directly applied by brush to spur leaves or petals of 'Braeburn' blossoms at pink bud, initial fruit set was only 23% that of untreated blossoms. lt is concluded that ammonium thiosulphate has the potential to thin apple blossoms. Further experiments to define optimum concentrations and spray volumes are needed

'Fantasia' Nectarine: Effects of Autumn-Applied Ethephon on Blossoming and Cropping

Ethephon was tested for its ability to delay blossoming in 'Fantasia' nectarine (Prunus persica (L.) Batsch). The effect on harvest date was also examined. Ethephon, at 50, 200, and 400 mg/litre, was applied as a spray either on 5 April or on 25 April 1985. All sprays delayed the onset of blossoming. The delay in reaching full blossom (>90% open blossoms) was 6-15 days for the first spray, and 14-16 days for the second spray. Ethephon, at 200 mg/litre, significantly increased the number of open blossoms on tagged branches. In addition, all ethephon treatments improved initial fruit set; 200 and 400 mg/litre treatments were most effective. Crop yield (in a low-yielding season) was 8 x greater on trees which had received 200 mg/litre ethephon than on non-treated trees. The blossom delay did not result in slower fruit growth, and did not affect the date of harvest maturity