Two algorithms for the student-project allocation problem

We study the Student-Project Allocation problem (SPA), a generalisation of the classical Hospitals / Residents problem (HR). An instance of SPA involves a set of students, projects and lecturers. Each project is offered by a unique lecturer, and both projects and lecturers have capacity constraints. Students have preferences over projects, whilst lecturers have preferences over students. We present two optimal linear-time algorithms for allocating students to projects, subject to the preference and capacity constraints. In particular, each algorithm finds a stable matching of students to projects. Here, the concept of stability generalises the stability definition in the HR context. The stable matching produced by the first algorithm is simultaneously best-possible for all students, whilst the one produced by the second algorithm is simultaneously best-possible for all lecturers. We also prove some structural results concerning the set of stable matchings in a given instance of SPA. The SPA problem model that we consider is very general and has applications to a range of different contexts besides student-project allocation

Maximum weight cycle packing in directed graphs, with application to kidney exchange programs

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration

Popular matchings with two-sided preferences and one-sided ties

We are given a bipartite graph $G = (A \cup B, E)$ where each vertex has a preference list ranking its neighbors: in particular, every $a \in A$ ranks its neighbors in a strict order of preference, whereas the preference lists of $b \in B$ may contain ties. A matching $M$ is popular if there is no matching $M'$ such that the number of vertices that prefer $M'$ to $M$ exceeds the number of vertices that prefer $M$ to~$M'$. We show that the problem of deciding whether $G$ admits a popular matching or not is NP-hard. This is the case even when every $b \in B$ either has a strict preference list or puts all its neighbors into a single tie. In contrast, we show that the problem becomes polynomially solvable in the case when each $b \in B$ puts all its neighbors into a single tie. That is, all neighbors of $b$ are tied in $b$'s list and $b$ desires to be matched to any of them. Our main result is an $O(n^2)$ algorithm (where $n = |A \cup B|$) for the popular matching problem in this model. Note that this model is quite different from the model where vertices in $B$ have no preferences and do not care whether they are matched or not.Comment: A shortened version of this paper has appeared at ICALP 201

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

Contact Networks and Mortality Patterns Suggest Pneumonia-Causing Pathogens may Persist in Wild Bighorn Sheep

Efficacy of disease control efforts is often contingent on whether the disease persists locally in the host population or is repeatedly introduced from an alternative host species. Local persistence is partially determined by the interaction between host contact structure and disease transmission rates: relatively isolated host groups facilitate pathogen persistence by slowing the rate at which highly transmissible pathogens access new susceptibles; alternatively, isolated host groups impede persistence for pathogens with low transmission rates by limiting the number of available hosts and forcing premature fade-out. Here, we use long-term data from the Hells Canyon region to investigate whether variable host contact patterns are associated with survival outcomes for 46 cohorts of bighorn sheep (Ovis canadensis) lambs subject to recurrent pneumonia outbreaks. We build social contact networks for each lamb cohort, and quantify variation in lamb mortality attributable to populations, years, and groups. We then refine estimates of chronic carriage rates in ewes, and disease-induced mortality rates in lambs, by finding parameters for the disease process that produce lamb morality rates similar to those observed when simulated on the observed host contact networks. Our results suggest that summer lamb hazards are spatially structured at the subpopulation level: 92.5 percent of the variation in lamb hazards during pneumonia outbreak years was attributable to sub-population-level groups, whereas 1.7 percent and 5.6 percent were attributable to year and population, respectively.  Additionally, the posterior distribution generated by our disease transmission model suggests that pneumonia-causing pathogens may persist locally in bighorn sheep populations, even during apparently healthy years

Disease Introduction Is Associated With a Phase Transition in Bighorn Sheep Demographics

Ecological theory suggests that pathogens are capable of regulating or limiting host population dynamics, and this relationship has been empirically established in several settings. However, although studies of childhood diseases were integral to the development of disease ecology, few studies show population limitation by a disease affecting juveniles. Here, we present empirical evidence that disease in lambs constrains population growth in bighorn sheep (Ovis canadensis) based on 45 years of population‐level and 18 years of individual‐level monitoring across 12 populations. While populations generally increased (λ = 1.11) prior to disease introduction, most of these same populations experienced an abrupt change in trajectory at the time of disease invasion, usually followed by stagnant‐to‐declining growth rates (λ = 0.98) over the next 20 years. Disease‐induced juvenile mortality imposed strong constraints on population growth that were not observed prior to disease introduction, even as adult survival returned to pre‐invasion levels. Simulations suggested that models including persistent disease‐induced mortality in juveniles qualitatively matched observed population trajectories, whereas models that only incorporated all‐age disease events did not. We use these results to argue that pathogen persistence may pose a lasting, but under‐recognized, threat to host populations, particularly in cases where clinical disease manifests primarily in juveniles

Integer programming methods for special college admissions problems

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones

2003, UMaine News Press Releases

This is a catalog of press releases put out by the University of Maine Division of Marketing and Communications between January 21, 2003 and September 15, 2003

Ecological interventions to prevent and manage zoonotic pathogen spillover

Spillover of a pathogen from awildlife reservoir into a human or livestock host requires the pathogen to overcome a hierarchical series of barriers. Interventions aimed at one or more of these barriers may be able to prevent the occurrence of spillover. Here, we demonstrate how interventions that target the ecological context in which spillover occurs (i.e. ecological interventions) can complement conventional approaches like vaccination, treatment, disinfection and chemical control. Accelerating spillover owing to environmental change requires effective, affordable, durable and scalable solutions that fully harness the complex processes involved in cross-species pathogen spillover. This article is part of the theme issue ‘Dynamic and integrative approaches to understanding pathogen spillover’