Related papers: Representing All Stable Matchings by Walking a Max…
Coherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension…
We consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an…
An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph $G = (A \cup B, E)$, with an adjacency list being a linearly ordered list of ties. Ties are subsets of vertices equally good…
Gale and Sotomayor (1985) have shown that in the Gale-Shapley matching algorithm (1962), the proposed-to side W (referred to as women there) can strategically force the W-optimal stable matching as the M-optimal one by truncating their…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
In this paper, we propose a new constraint, called shift-consistency, for solving matrix/tensor completion problems in the context of recommender systems. Our method provably guarantees several key mathematical properties: (1) satisfies a…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). In particular, we seek stable matchings that are optimal with respect to profile, which is a vector that indicates the…
This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and…
The Stable Roommates problems are characterized by the preferences of agents over other agents as roommates. A solution is a partition of the agents into pairs that are acceptable to each other (i.e., they are in the preference lists of…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…
We provide rigorous proofs that the Integrated Gradients (IG) attribution method for deep networks satisfies completeness and symmetry-preserving properties. We also study the uniqueness of IG as a path method preserving symmetry.
In an effort to effectively model observed patterns in the spatial configuration of individuals of multiple species in nature, we introduce the saturated pairwise interaction Gibbs point process. Its main strength lies in its ability to…
The graph matching problem aims to discover a latent correspondence between the vertex sets of two observed graphs. This problem has proven to be quite challenging, with few satisfying methods that are computationally tractable and widely…