The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with quantitative preferences: each man (resp., woman) provides a score for each woman (resp., man). Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations it is more natural to express scores (to model, for example, profits or costs) rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages which are stable and/or optimal according to these notions. While expressivity greatly increases by adopting quantitative preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

A common problem faced by expanding companies is the lack of skilled and experienced domain experts, especially planners and controllers. This can seriously slow down or impede growth. This paper describes how we worked with one of the largest travel agencies in Hong Kong to alleviate this problem by using AI to support decision-making and problem-solving so that their planners/controllers can be more productive in sustaining business growth while providing quality service. This paper describes a Web-based mission critical Fleet Management System (FMS) that supports the scheduling and management of a fleet of luxury limousines. Clientele is mainly business travelers. The use of AI allowed our client to increase their business volume and expand fleet size with the same team of planners/controllers while maintaining service quality. This paper also describes our experience in building modern AI systems leveraging on Web 2.0 open-source tools and libraries. Although we used a proven AI model and search algorithm, we believe our innovation is in striking the right balance and combination of AI with modern Web 2.0 techniques to achieve low-risk implementation and deployment success as well as concrete and measurable business benefits.

We present a highly efficient incremental algorithm for propagating bounded knapsack constraints. Our algorithm is based on the sublinear filtering algorithm for binary knapsack constraints by Katriel et al. and achieves similar speed-ups of one to two orders of magnitude when compared with its linear-time counterpart. We also show that the representation of bounded knapsacks as binary knapsacks leads to ineffective filtering behavior. Experiments on standard knapsack benchmarks show that the new algorithm significantly outperforms existing methods for handling bounded knapsack constraints.

Planning as satisfiability is a principal approach to planning with many eminent advantages. The existing planning as satisfiability techniques usually use encodings compiled from the STRIPS formalism. We introduce a novel SAT encoding scheme based on the SAS+ formalism. It exploits the structural information in the SAS+ formalism, resulting in more compact SAT instances and reducing the number of clauses by up to 50 fold. Our results show that this encoding scheme improves upon the STRIPS-based encoding, in terms of both time and memory efficiency.

Many problems in AI, including planning, logical reasoning and probabilistic inference, have been shown to reduce to (weighted) constraint satisfaction. While there are a number of approaches for solving such problems, the recent gains in efficiency of the satisfiability approach have made SAT solvers a popular choice. Modern propositional SAT solvers are efficient for a wide variety of problems. However, particularly in the case of spatial reasoning, conversion to propositional SAT can sometimes result in a large number of variables and/or clauses. Moreover, spatial reasoning problems can often be more efficiently solved if the agent is able to exploit the geometric nature of space to make better choices during search and backtracking. The result of these two drawbacks — larger problem sizes and inefficient search — is that even simple spatial constraint problems are often intractable in the SAT approach. In this paper we propose a spatial reasoning system that provides significant performance improvements in constraint satisfaction problems involving spatial predicates. The key to our approach is to integrate a diagrammatic representation with a DPLL-based backtracking algorithm that is specialized for spatial reasoning. The resulting integrated system can be applied to larger and more complex problems than current approaches and can be adopted to improve performance in a variety of problems ranging from planning to probabilistic inference

We consider the task of assigning experts from a portfolio of specialists in order to solve a set of tasks. We apply a Bayesian model which combines collaborative filtering with a feature-based description of tasks and experts to yield a general framework for managing a portfolio of experts. The model learns an embedding of tasks and problems into a latent space in which affinity is measured by the inner product. The model can be trained incrementally and can track non-stationary data, tracking potentially changing expert and task characteristics. The approach allows us to use a principled decision theoretic framework for expert selection, allowing the user to choose a utility function that best suits their objectives. The model component for taking into account the performance feedback data is pluggable, allowing flexibility. We apply the model to manage a portfolio of algorithms to solve hard combinatorial problems. This is a well studied area and we demonstrate a large improvement on the state of the art in one domain (constraint solving) and in a second domain (combinatorial auctions) created a portfolio that performed significantly better than any single algorithm.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R ( *,m ) C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR ( *,m ) C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tightening the existing relations and without introducing new ones. We empirically show that wR(*,m)C solves in a backtrack-free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.

We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.

We develop an efficient algorithm for computing pure strategy Nash equilibria that satisfy various criteria (such as the utilitarian or Nash-Bernoulli social welfare functions) in games with sparse interaction structure. Our algorithm, called Valued Nash Propagation (VNP), integrates the optimisation problem of maximising a criterion with the constraint satisfaction problem of finding a game's equilibria to construct a criterion that defines a c -semiring. Given a suitably compact game structure, this criterion can be efficiently optimised using message-passing. To this end, we first show that VNP is complete in games whose interaction structure forms a hypertree. Then, we go on to provide theoretic and empirical results justifying its use on games with arbitrary structure; in particular, we show that it computes the optimum >82% of the time and otherwise selects an equilibrium that is always within 2% of the optimum on average.

Machine learning and data mining have become aware that using constraints when learning patterns and rules can be very useful. To this end, a large number of special purpose systems and techniques have been developed for solving such constraint-based mining and learning problems. These techniques have, so far, been developed independently of the general purpose tools and principles of constraint programming known within the field of artificial intelligence. This paper shows that off-the-shelf constraint programming techniques can be applied to various pattern mining and rule learning problems (cf. also (De Raedt, Guns, and Nijssen 2008; Nijssen, Guns, and De Raedt 2009)). This does not only lead to methodologies that are more general and flexible, but also provides new insights into the underlying mining problems that allow us to improve the state-of-the-art in data mining. Such a combination of constraint programming and data mining raises a number of interesting new questions and challenges.