The stable roommates problem with ties

We study the variant of the well-known stable roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear–time algorithm for finding a super-stable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NP-hardness of the analogous problem under weak stability. We also extend our algorithm to cope with preference lists that are incomplete and/or partially ordered. On the other hand, for a given stable roommates instance with ties and incomplete lists, we show that the weakly stable matchings may be of different sizes and the problem of finding a maximum cardinality weakly stable matching is NP-hard, though approximable within a factor of 2

Stem and progenitor cells: Origins, phenotypes, lineage commitments, and transdifferentiations

Multipotent stem cells are clonal cells that self-renew as well as differentiate to regenerate adult tissues. Whereas stem cells and their fates are known by unique genetic marker studies, the fate and function of these cells are best studied by their prospective isolation. This review is about the properties of various highly purified tissue-specific multipotent stem cells and purified oligolineage progenitors. We contend that unless the stem or progenitor cells in question have been purified to near homogeneity, one cannot know whether their generation of expected (or unexpected) progeny is a property of a known cell type. It is interesting that in the hematopoietic system the only long-term self-renewing cells in the stem and progenitors pool are the hematopoietic stem cells. This fact is discussed in the context of normal and leukemic hematopoiesis

An Algorithm for a Super-Stable Roommates Problem

In this paper we describe an efficient algorithm that decides if a stable matching exists for a generalized stable roommates problem, where, instead of linear preferences, agents have partial preference orders on potential partners. Furthermore, we may forbid certain partnerships, that is, we are looking for a matching such that none of the matched pairs is forbidden, and yet, no blocking pair (forbidden or not) exists. To solve the above problem, we generalize the first algorithm for the ordi- nary stable roommates problem

Quality Improvement in Health Care: A Framework for Price and Output Measurement

The durability of health care treatment, the substantial technical change in health care treatment, and the prevalence of third-party payment interact to create substantial difficulty in measuring the price and output of health care. This paper provides a framework for analyzing the demand for health care taking into account these difficulties. It then suggests how this framework might be used to improve measurement of health care prices and output.

Guest editorial: Special issue on matching under preferences

No abstract available

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, egald-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+372d+37-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

Progress in InP solar cell research

Progress, in the past year, in InP solar cell research is reviewed. Small area cells with AMO, total area efficiencies of 18.8 percent were produced by OMCVD and Ion Implantation. Larger area cells (2 and 4 sq cm) were processed on a production basis. One thousand of the 2 sq cm cells will be used to supply power to a small piggyback lunar orbiter scheduled for launch in February 1990. Laboratory tests of ITO/InP cells, under 10 MeV proton irradiation, indicate radiation resistance comparable to InP n/p homojunction cells. Computer modeling studies indicate that, for identical geometries and dopant concentrations, InP solar cells are significantly more radiation resistant than GaAs under 1 MeV electron irradiation. Additional computer modeling calculations were used to produce rectangular and circular InP concentrator cell designs for both the low concentration SLATS and higher concentration Cassegrainian Concentrators

Stable Marriage with Ties and Bounded Length Preference Lists

We consider variants of the classical stable marriage problem in which preference lists may contain ties, and may be of bounded length. Such restrictions arise naturally in practical applications, such as centralised matching schemes that assign graduating medical students to their first hospital posts. In such a setting, weak stability is the most common solution concept, and it is known that weakly stable matchings can have different sizes. This motivates the problem of finding a maximum cardinality weakly stable matching, which is known to be NP-hard in general. We show that this problem is solvable in polynomial time if each man's list is of length at most 2 (even for women's lists that are of unbounded length). However if each man's list is of length at most 3, we show that the problem becomes NP-hard and not approximable within some d > 1, even if each woman's list is of length at most 4

Heteroepitaxial InP solar cells on Si and GaAs substrates

The characteristics of InP cells processed from thin layers of InP heteroepitaxially grown on GaAs, on silicon with an intervening GaAs layer, and on GaAs with intervening Ga(x)In(1-x)As layers are described, and the factors affecting cell efficiency are discussed. Under 10 MeV proton irradiations, the radiation resistances of the heteroepitaxial cells were superior to that of homoepitaxial InP cells. The superior radiation resistance is attributed to the high dislocation densities present in the heteroepitaxial cells