Related papers: Colourful matchings
In frequently repeated matching scenarios, individuals may require diversification in their choices. Therefore, when faced with a set of potential outcomes, each individual may have an ideal lottery over outcomes that represents their…
In this paper, we study three matching problems all of which came up quite recently in the field of machine teaching. The cost of a matching is defined in such a way that, for some formal model of teaching, it equals (or bounds) the number…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
We consider a committee voting setting in which each voter approves of a subset of candidates and based on the approvals, a target number of candidates are selected. Aziz et al. (2015) proposed two representation axioms called justified…
We introduce the concept of a threefold Post correspondence system (3PCS for short) and we consider it as an instance of the threefold Post correspondence problem. With each 3PCS, we associate three Post correspondence systems, i.e., three…
The popular matching problem is of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in the order of preference, possibly with ties. A matching M is popular if…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
Matching mechanisms play a central role in operations management across diverse fields including education, healthcare, and online platforms. However, experimentally comparing a new matching algorithm against a status quo presents some…
In the {\sc Course Allocation} problem, there are a set of students and a set of courses at a given university. University courses may have different numbers of credits, typically related to different numbers of learning hours, and there…
This paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. First, we show by means of an example that a…
Compositionality supports the manipulation of large systems by working on their components. For model-based testing, this means that large systems can be tested by modelling and testing their components: passing tests for all components…
Modern software systems, like GNU/Linux distributions or Eclipse-based development environment, are often deployed by selecting components out of large component repositories. Maintaining such software systems by performing component…
This paper studies two-sided many-to-one matching in which firms have complementary preferences. We show that stable matchings exist under a balancedness condition that rules out a specific type of odd-length cycles formed by firms'…
With the prevalence of deep learning based embedding approaches, recommender systems have become a proven and indispensable tool in various information filtering applications. However, many of them remain difficult to diagnose what aspects…
We study two-stage committee elections where voters have dynamic preferences over candidates; at each stage, a committee is chosen under a given voting rule. We are interested in identifying a winning committee for the second stage that…
Building fair recommender systems is a challenging and crucial area of study due to its immense impact on society. We extended the definitions of two commonly accepted notions of fairness to recommender systems, namely equality of…
We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A U P,E), where A denotes a set of applicants, P is a set of posts, and there are…
List colouring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-colouring, we seek many in parallel. Our explorations have uncovered a…
This paper studies a decentralized many-to-one matching market where preferences remain uncertain during the matching process. Institutions initiate matching by sending offers, and applicants decide whether to accept upon receiving them.…
Consider elections where the set of candidates is partitioned into parties, and each party must nominate exactly one candidate. The Possible President problem asks whether some candidate of a given party can become the winner of the…