Related papers: On stable assignments generated by choice function…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
Stable matching in a community consisting of men and women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley, who…
Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whereas the second contains two fractional derivatives. Such…
Many allocation problems in multiagent systems rely on agents specifying cardinal preferences. However, allocation mechanisms can be sensitive to small perturbations in cardinal preferences, thus causing agents who make ``small" or…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
The assignment of personnel to teams is a fundamental and ubiquitous managerial function, typically involving several objectives and a variety of idiosyncratic practical constraints. Despite the prevalence of this task in practice, the…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
We generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of…
In mathematics education research, mathematics task sets involving mixed practice include tasks from many different topics within the same assignment. In this paper, we use graph decompositions to construct mixed practice task sets for…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
Gale and Shapley's stable assignment problem has been extensively studied, applied, and extended. In the context of school choice, mechanisms often aim at finding an assignment that is more favorable to students. We investigate two…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
This paper addresses the bipartite consensus-control problem in open multi-agent systems containing both cooperative and antagonistic interactions. In these systems, new agents can join and new interactions can be formed over time.…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and…
Task allocation has been a well studied problem. In most prior problem formulations, it is assumed that each task is associated with a unique set of resource requirements. In the scope of multi-robot task allocation problem, these…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
We study the many-to-many bipartite matching problem in the presence of preferences where ties, as well as lower quotas, may appear on both sides of the bipartition. The input is a bipartite graph $G=(A \cup B, E)$, where each vertex in $A…