Modelling and Solving the Stable Marriage Problem Using Constraint Programming

We study the Stable Marriage problem (SM), which is a combinatorial problem that arises in many practical applications. We present two new models of an instance I of SM with n men and n women as an instance J of a Constraint Satisfaction Problem. We prove that establishing arc consistency in J yields the same structure as given by the established Extended Gale/Shapley algorithm for SM as applied to I. Consequently, a solution (stable matching) of I can be derived without search. Furthermore we show that, in both encodings, all stable matchings in I may be enumerated in a failure-free manner. Our first encoding is of O(n^3) complexity and is very natural, whilst our second model, of O(n^2) complexity (which is optimal), is a development of the Boolean encoding in [6], establishing a greater level of structure

Student-Project Allocation with Preferences over Projects

We study the problem of allocating students to projects, where both students and lecturers have preferences over projects, and both projects and lecturers have capacities. In this context we seek a stable matching of students to projects, which respects these preference and capacity constraints. Here, the stability definition generalises the corresponding notion in the context of the classical Hospitals / Residents problem. We show that stable matchings can have different sizes, and the problem of finding a maximum cardinality stable matching is NP-hard, though approximable within a factor of 2

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

A Constraint Programming Approach to the Hospitals / Residents Problem

An instance I of the Hospitals / Residents problem (HR) involves a set of residents (graduating medical students) and a set of hospitals, where each hospital has a given capacity. The residents have preferences for the hospitals, as do hospitals for residents. A solution of I is a stable matching, which is an assignment of residents to hospitals that respects the capacity conditions and preference lists in a precise way. In this paper we present constraint encodings for HR that give rise to important structural properties. We also present a computational study using both randomly-generated and real-world instances. Our study suggests that Constraint Programming is indeed an applicable technology for solving this problem, in terms of both theory and practice

University and the State in Ireland: from a negotiated exchange relationship based on trust to prescriptive requirements in university governance

This study examines the governance of Irish universities over the past thirty years and in particular how the governance of the Irish university system has moved from a model based on a trust and exchange relationship between the universities and the State to one where the universities are themselves State agencies, directed by a paymaster State to deliver State policy objectives in a number of areas. These include economic development, re-skilling of workers and the exploitation of academic outcomes. Looking through a lens of trust, informed by an analysis of the relevant literature, changes in governance, accountability and autonomy in the Irish State/university relationship since 1980 have been examined and documented. The emergence of professional management in universities and the related decline in the power of the academic community together with the transfer of overall direction of the institution from Senate or Academic Council to corporatist style governing bodies is documented. This is done against a background of the emerging evaluative State which measures performance against objectives which it sets down and which creates a new bureaucracy to measure, manage and control all State enterprise and investment. The Maynooth Archive has been used as a primary source of evidence for this claim. Utilising the eight key areas identified by the OECD in 2003 as key to university autonomy, the archive is reviewed over the thirty years by an analysis of the actual decisions made and the different kinds of interactions between the State and the governing body at Maynooth. Set against a background of government investment in universities and the wide-ranging international discourse on university governance, a ‘Governance and Accountability Framework’ has been developed which traces the move from autonomous university institution to directed State agency. The experience of key personnel in the Irish universities is then explored, on the basis of a series of semi structured interviews, to gain a deeper understanding of how universities are experiencing the changes that are taking place in the governance of Irish universities. Each of the seven Presidents participated in a semi-structured interview on the emerging changes in university governance and their views are analysed around a number of common themes. Similarly four key senior State personnel playing significant roles in the governance of the universities in Ireland participated in a semi-structured interview and their views are analysed using the same themes as those used to analyse the Presidents interviews. This provided an insight into the State position on the related issues of trust, accountability and autonomy. This analysis, drawing on the insights gleaned from both the archive study and the interviews allowed for a triangulation of the theme findings leading to a conclusion that a new paradigm has emerged in the university/State relationship. This is one where the university has been co-opted by the State to deliver on key elements of the State agenda. This thesis suggests that as the State began to look at knowledge as a key factor of economic growth it turned to the universities as the main producers and disseminators of knowledge. Accordingly as the role of the university has changed so too has the regulatory and supervisory environment in which they must work. This thesis concludes that the key element, lacking from and necessary to this process, is that of trust and that the relationship between university and State needs to be reconfigured in a way that crucially attempts to re-empower the academy while recognising that sustainability is dependent on a less than benevolent State

Modelling and Solving the Stable Marriage Problem Using Constraint Programming

We study the Stable Marriage problem (SM), which is a combinatorial problem that arises in many practical applications. We present two new models of an instance I of SM with n men and n women as an instance J of a Constraint Satisfaction Problem. We prove that establishing arc consistency in J yields the same structure as given by the established Extended Gale/Shapley algorithm for SM as applied to I. Consequently, a solution (stable matching) of I can be derived without search. Furthermore we show that, in both encodings, all stable matchings in I may be enumerated in a failure-free manner. Our first encoding is of O(n^3) complexity and is very natural, whilst our second model, of O(n^2) complexity (which is optimal), is a development of the Boolean encoding in [6], establishing a greater level of structure

Second-chance punitivism and the contractual governance of crime and incivility: New Labour, old Hobbes

The growing application of mechanisms of contractual governance to behaviour that breaches social norms, rather than the criminal law, appears to represent an ethopolitical concern with delinquent self-reform through the activation of technologies of the self. In fact, there is little empirical evidence that the contractual governance of incivility leads to such self-reform. Beneath the ideology of contractual agreement to observe social norms lies what this paper calls a ‘second-chance punitivism’ which operates to crystallise behavioural elements of the Hobbesian social contract, after breach, into a more specific form. The responsibilising and individualising properties of this form of contractual governance set the moral-ideological platform for a retributive punitivism, when the rational agents it creates fail to live up to their image, and are taken to have wasted their ‘second chance’

Student-project allocation with preferences over projects

We study the problem of allocating students to projects, where both students and lecturers have preferences over projects, and both projects and lecturers have capacities. In this context we seek a stable matching of students to projects, which respects these preference and capacity constraints. Here, the stability definition generalises the corresponding notion in the context of the classical Hospitals/Residents problem. We show that stable matchings can have different sizes, which motivates max-spa-p, the problem of finding maximum cardinality stable matching. We prove that max-spa-p is NP-hard and not approximable within δ, for some δ>1, unless P=NP. On the other hand, we give an approximation algorithm with a performance guarantee of 2 for max-spa-p

Frequency response from aggregated V2G chargers with uncertain EV connections

Fast frequency response (FR) is highly effective at securing frequency dynamics after a generator outage in low inertia systems. Electric vehicles (EVs) equipped with vehicle to grid (V2G) chargers could offer an abundant source of FR in future. However, the uncertainty associated with V2G aggregation, driven by the uncertain number of connected EVs at the time of an outage, has not been fully understood and prevents its participation in the existing service provision framework. To tackle this limitation, this paper, for the first time, incorporates such uncertainty into system frequency dynamics, from which probabilistic nadir and steady state frequency requirements are enforced via a derived moment-based distributionally-robust chance constraint. Field data from over 25,000 chargers is analysed to provide realistic parameters and connection forecasts to examine the value of FR from V2G chargers in annual operation of the GB 2030 system. The case study demonstrates that uncertainty of EV connections can be effectively managed through the proposed scheduling framework, which results in annual savings of Misplaced &6,300 or 37.4 tCO2 per charger. The sensitivity of this value to renewable capacity and FR delays is explored, with V2G capacity shown to be a third as valuable as the same grid battery capacity

Marijuana and Youth

This paper contains the first estimates of the price sensitivity of the prevalence of youth marijuana use. Survey data on marijuana use by high school seniors from the Monitoring the Future Project are combined with data on marijuana prices and potency from the Drug Enforcement Administration Office of Intelligence or Intelligence Division. Our estimates of the price elasticity of annual marijuana participation range from 0.06 to 0.47, while those for thirty day participation range from 0.002 to 0.69. These estimates clearly imply that changes in the real, quality adjusted price of marijuana contributed significantly to the trends in youth marijuana use between 1982 and 1998, particularly during the contraction in use from 1982 to 1992. Similarly, changes in youth perceptions of the harms associated with regular marijuana use had a substantial impact on both the contraction in use during the 1982 though 1992 period and the subsequent expansion in use after 1992. These findings underscore the usefulness of considering price in addition to more traditional determinants in any analysis of marijuana consumption decisions made by youths.