In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social welfare, since the values of the agents remain virtually unknown. This loss in performance because of lack of information is measured by distortion. A recent array of works put forward the agenda of designing mechanisms that learn the values of the agents for a small number of alternatives via queries, and use this limited extra information to make better-informed decisions, thus improving distortion. Following this agenda, in this work we focus on a class of combinatorial problems that includes most well-known matching problems and several of their generalizations, such as One-Sided Matching, Two-Sided Matching, General Graph Matching, and k-Constrained Resource Allocation. We design two-query mechanisms that achieve the best-possible worst-case distortion in terms of social welfare, and outperform the best-possible expected distortion achieved by randomized ordinal mechanisms.

We study a many-to-one matching problem, such as the college admission problem, where each college can admit multiple students. Unlike classical models, colleges evaluate sets of students through non-linear utility functions that capture diversity between them. In this setting, we show that classical stable matchings may fail to exist. To address this, we propose alternative solution concepts based on Rawlsian fairness, aiming to maximize the minimum utility across colleges. We design both deterministic and stochastic algorithms that iteratively improve the outcome of the worst-off college, offering a practical approach to fair allocation when stability cannot be guaranteed.

This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one optimal, to solve this problem. We also generate a benchmark to cover different instances of SSMP varying in complexity, and carry out an experimental evaluation to assess the performance of the approaches.

In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social welfare, since the values of the agents remain virtually unknown. This loss in performance because of lack of information is measured by distortion. A recent array of works put forward the agenda of designing mechanisms that learn the values of the agents for a small number of alternatives via queries, and use this limited extra information to make better-informed decisions, thus improving distortion. Following this agenda, in this work we focus on a class of combinatorial problems that includes most well-known matching problems and several of their generalizations, such as One-Sided Matching, Two-Sided Matching, General Graph Matching, and k-Constrained Resource Allocation.

Due to the large number of submissions that more and more conferences experience, finding an automatized way to well distribute the submitted papers among reviewers has become necessary. We model the peer-reviewing matching problem as a {\it bilevel programming (BP)} formulation. Our model consists of a lower-level problem describing the reviewers' perspective and an upper-level problem describing the editors'. Every reviewer is interested in minimizing their overall effort, while the editors are interested in finding an allocation that maximizes the quality of the reviews and follows the reviewers' preferences the most. To the best of our knowledge, the proposed model is the first one that formulates the peer-reviewing matching problem by considering two objective functions, one to describe the reviewers' viewpoint and the other to describe the editors' viewpoint. We demonstrate that both the upper-level and lower-level problems are feasible and that our BP model admits a solution under mild assumptions. After studying the properties of the solutions, we propose a heuristic to solve our model and compare its performance with the relevant state-of-the-art methods. Extensive numerical results show that our approach can find fairer solutions with competitive quality and less effort from the reviewers.

Many various types of sensors coming from different complex devices collect data from a city. Their underlying data representation follows specific manufacturer specifications that have possibly incomplete descriptions (in ontology) alignments. This paper addresses the problem of determining accurate and complete matching of ontologies given some common descriptions and their pre-determined high level alignments. In this context the problem of ontology matching consists of automatically determining all matching given the latter alignments, and manually verifying the matching results. Especially for applications where it is crucial that ontologies are matched correctly the latter can turn into a very time-consuming task for the user. This paper tackles this challenge and addresses the problem of computing the minimum number of user inputs needed to verify all matchings. We show how to represent this problem as a reasoning problem over a bipartite graph and how to encode it over pseudo Boolean constraints. Experiments show that our approach can be successfully applied to real-world data sets.

Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in practice. Here, we investigate if this difficulty can be mitigated when some additional piece of information is available: (a) that all QAP instances of interest come from the same application, and (b) the correct solution for a set of such QAP instances is given. We propose a new approach to accelerate the solution of QAPs based on learning parameters for a modified objective function from prior QAP instances. A key feature of our approach is that it takes advantage of the algebraic structure of permutations, in conjunction with special methods for optimizing functions over the symmetric group Sn in Fourier space. Experiments show that in practical domains the new method can outperform existing approaches.