Related papers: On stable assignments generated by choice function…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…
We provide a framework for the assignment of multiple robots to goal locations, when robot travel times are uncertain. Our premise is that time is the most valuable asset in the system. Hence, we make use of redundant robots to counter the…
Recently, the saturation problem of $0$-$1$ matrices gained a lot of attention. This problem can be regarded as a saturation problem of ordered bipartite graphs. Motivated by this, we initiate the study of the saturation problem of ordered…
The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…
Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…
In this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of contracts to choose from. We call such problems, contract choice problems. We provide conditions…
We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices $i\in I$ are interpreted as agents, and the edges $c\in C$ as contracts that can be concluded between agents. The preferences of each agent…
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…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
This work addresses the problem of assigning periodic tasks to workers in a balanced way, i.e., so that each worker performs every task with the same frequency over the long term. The input consists of a list of tasks to be repeated weekly…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where…
In two-sided matching markets with contracts, quantile (or generalized median) stable mechanisms represent an interesting class that produces stable allocations which can be viewed as compromises between both sides of the market. These…
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a…