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

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

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

From Marriages to Coalitions: A Soft CSP Approach

In this workwerepresent the Optimal Stable Marriage problem as a Soft Constraint Satisfaction Problem. In addition, we extend this problem from couples of individuals to coalitions of generic agents, in order to define new coalition-formation principles and stability conditions. In the coalition case, we suppose the preference value as a trust score, since trust can describe a nodes belief in another nodes capabilities, honesty and reliability. Soft constraints represent a general and expressive framework that is able to deal with distinct concepts of optimality by only changing the related c-semiring structure, instead of using di erent ad-hoc algorithms. At last, we propose an implementation of the classical OSM problem by using Integer Linear Programming tools

Revisiting two-sided stability constraints

We show that previous filtering propositions on two-sided stability problems do not enforce arc consistency (AC), however they maintain Bound(D) Consistency (BC(D)). We propose an optimal algorithm achieving BC(D) with O(L) time complexity where L is the length of the preference lists. We also show an adaptation of this filtering approach to achieve AC. Next, we report the first polynomial time algorithm for solving the hospital/resident problem with forced and forbidden pairs. Furthermore, we show that the particular case of this problem for stable marriage can be solved in O(n2) which improves the previously best complexity by a factor of n2. Finally, we present a comprehensive set of experiments to evaluate the filtering propositions

Industry Life Cycle and the Evolution of an Industry Network

This paper addresses the problem of the general validity of models of the industry life cycle, which have been proposed to analyse the long-term evolution of many industries, exhibiting a typical pattern of shakeout. We study a case of non shake-out in the commercial jet aero-engine industry, marked by a small number of entry events distributed over 40 years of industry evolution, by no exits and by a resulting slowly increasing number of firms. We argue that the vertical structure of the industry, as represented by the network of vertical relations between aero-engine suppliers and aircraft manufacturers, "regulated" the process of entry and exit and posed the conditions for a non shakeout to take place.industry life cycle; entry, exit; network; vertical relations