A specialised constraint approach for stable matching problems

Constraint programming is a generalised framework designed to solve combinatorial problems. This framework is made up of a set of predefined independent components and generalised algorithms. This is a very versatile structure which allows for a variety of rich combinatorial problems to be represented and solved relatively easily. Stable matching problems consist of a set of participants wishing to be matched into pairs or groups in a stable manner. A matching is said to be stable if there is no pair or group of participants that would rather make a private arrangement to improve their situation and thus undermine the matching. There are many important "real life" applications of stable matching problems across the world. Some of which includes the Hospitals/Residents problem in which a set of graduating medical students, also known as residents, need to be assigned to hospital posts. Some authorities assign children to schools as a stable matching problem. Many other such problems are also tackled as stable matching problems. A number of classical stable matching problems have efficient specialised algorithmic solutions. Constraint programming solutions to stable matching problems have been investigated in the past. These solutions have been able to match the theoretically optimal time complexities of the algorithmic solutions. However, empirical evidence has shown that in reality these constraint solutions run significantly slower than the specialised algorithmic solutions. Furthermore, their memory requirements prohibit them from solving problems which the specialised algorithmic solutions can solve in a fraction of a second. My contribution investigates the possibility of modelling stable matching problems as specialised constraints. The motivation behind this approach was to find solutions to these problems which maintain the versatility of the constraint solutions, whilst significantly reducing the performance gap between constraint and specialised algorithmic solutions. To this end specialised constraint solutions have been developed for the stable marriage problem and the Hospitals/Residents problem. Empirical evidence has been presented which shows that these solutions can solve significantly larger problems than previously published constraint solutions. For these larger problem instances it was seen that the specialised constraint solutions came within a factor of four of the time required by algorithmic solutions. It has also been shown that, through further specialisation, these constraint solutions can be made to run significantly faster. However, these improvements came at the cost of versatility. As a demonstration of the versatility of these solutions it is shown that, by adding simple side constraints, richer problems can be easily modelled. These richer problems add additional criteria and/or an optimisation requirement to the original stable matching problems. Many of these problems have been proven to be NP-Hard and some have no known algorithmic solutions. Included with these models are results from empirical studies which show that these are indeed feasible solutions to the richer problems. Results from the studies also provide some insight into the structure of these problems, some of which have had little or no previous study

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 <i>stable matching</i>, 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. We provide additional motivation for our models by indicating how side constraints can be added easily in order to solve hard variants of HR

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

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

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

Answer Set Programming Modulo `Space-Time'

We present ASP Modulo `Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of `space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks

Growth, Conventional Production and Tourism Specialisation: Technological Catching-up Versus Terms-of-Trade Effects

This paper extends the ’expanding-varieties’ growth model in a two-countries-two-goods setup, and describes the dynamics of growth rates and terms of trade when the industry-based economy is the innovation leader, while the tourism-based economy is the follower (i.e. increases the number of intermediate inputs by readapting innovations developed abroad). Two types of transitional dynamics may exist: technological catching-up and technological falling-behind. Contrary to the standard result, technological catching-up by the follower is associated with lower growth rates with respect to the leader, whereas terms-of-trade effects guarantee positive growth differentials for the tourism-based economy when the technological gap with the leader increases over time. The underlying principle of ’increased relative demand’ might explain the good economic performance observed in tourism-dependent economies.Endogenous growth, Two-country models, Technology diffusion, Trade specialization

Urban Governance and Finance in India

Over 330 million people live in Indias cities; 35 cities have a population of over a million and three (Mumbai, Delhi, and Kolkata) of the 10 largest metropolises in the world are in India. Indias cities are large, economically important, and growing. However, neither urban infrastructure nor the level of urban public services is adequate for current needs, let alone to meet growing demands. Dealing with this problem is a formidable challenge. Not only must adequate finance for the provision of services be found but it is critical to ensure that the money spent results in desired outputs and outcomes. To do so, local governance structures also need to be reformed and strengthened. This paper attempts to point the way towards some possible solutions by analysing urban governance and finance in India in the context of lessons drawn from fiscal federalism theory and experiences of governance institutions and financing systems both in India and around the world. No one system of urban governance is likely to work equally well for all urban local bodies. However, the paper identifies some key reforms required to realise both the constitutional intent to encourage citizen participation in urban governance and the economic and politically desirable goal of ensuring greater accountability of urban governments. For example, the paper draws attention to existing ambiguities in the assignment system and underlines the need to undertake activity mapping to ensure clarity as well as to make independent agencies significantly accountable to elected governments in urban areas. The paper also discusses a variety of ways of augmenting the resources of the municipal bodies in the country including essential reforms in the property tax system and adequate exploitation of user charges and fees for various services delivered as well as ways of strengthening and improving Central and State transfers to urban local governments. With respect to financing urban infrastructure, development charges should be used more effectively. More should also be done to utilise public lands more effectively. In addition, to a considerable extent capital expenditure requirements will have to be financed through borrowing so further development of the municipal bond market is important, as is more and more effective use of public private partnerships in some areas.India, urban public finance, urban governance, intergovernmental fiscal relations, property tax, Metropolitan areas, infrastructure finance