Related papers: Stable Fractional Matchings
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…
In many-to-many matching models, substitutable preferences constitute the largest domain for which a pairwise stable matching is guaranteed to exist. In this note, we extend the recently proposed algorithm of Hatfield et al. [3] to test…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.
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…
The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
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 consider an identification problem, where the state $u$ is governed by a fractional elliptic equation and the unknown variable corresponds to the order $s \in (0,1)$ of the underlying operator. We study the existence of an optimal pair…
Submodular maximization with a cardinality constraint can model various problems, and those problems are often very large in practice. For the case where objective functions are monotone, many fast approximation algorithms have been…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
It is preferred that feature selectors be \textit{stable} for better interpretabity and robust prediction. Ensembling is known to be effective for improving the stability of feature selectors. Since ensembling is time-consuming, it is…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of…
When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may…
Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…
The Gale-Shapley algorithm for the Stable Marriage Problem is known to take $\Theta(n^2)$ steps to find a stable marriage in the worst case, but only $\Theta(n \log n)$ steps in the average case (with $n$ women and $n$ men). In 1976, Knuth…
We generalize several schedule matching theorems of Baiou-Balinski (Math. Oper. Res., 27 (2002), 485) and Alkan-Gale (J. Econ. Th. 112 (2003), 289) by applying a fixed point method of Fleiner (Math. Oper. Res., 28 (2003), 103). Thanks to a…