Related papers: Computational complexity of $k$-stable matchings
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
We highlight the tension between stability and equality in non transferable utility matching. We consider many to one matchings and refer to the two sides of the market as students and schools. The latter have aligned preferences, which in…
Following up a recent work by Ashlagi, Kanoria and Leshno, we study a stable matching problem with unequal numbers of men and women, and independent uniform preferences. The asymptotic formulas for the expected number of stable matchings,…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…
Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of k matrices in R^{n x n} are stable. In particular, we are interested whether there exist…
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…
In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley. In this article, we try to find…
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 say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
In many labor markets, workers and firms are connected via affiliative relationships. A management consulting firm wishes to both accept the best new workers but also place its current affiliated workers at strong firms. Similarly, a…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the…
In 1976, Knuth asked if the stable marriage problem (SMP) can be generalized to marriages consisting of 3 genders. In 1988, Alkan showed that the natural generalization of SMP to 3 genders ($3$GSM) need not admit a stable marriage. Three…
Motivated by the increasing interest in the explicit representation and handling of various "preference" structures arising in modern digital economy, this work introduces a new class of "one-to-many stable-matching" problems where a set of…
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…
We consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching…
We study a matching problem between agents and public goods, in settings without monetary transfers. Since goods are public, they have no capacity constraints. There is no exogenously defined budget of goods to be provided. Rather, each…