Related papers: Twenty Open Problems in Enumeration of Matchings: …
Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the…
This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.
We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on "Arithmetic Topology". Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
Enumerating matchings is a classical problem in the field of enumeration algorithms. There are polynomial-delay enumeration algorithms for several settings, such as enumerating perfect matchings, maximal matchings, and (weighted) matchings…
In recent years, significant advances have been made in the design and analysis of fully dynamic maximal matching algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the…
Decoupling is a recent development in Fourier analysis, which has applications in harmonic analysis, PDE, and number theory. We survey some applications of decoupling and some of the ideas in the proof. This survey is aimed at a general…
Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the…
This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…
This dissertation collects together results on Patience Sorting and its generalizations. It incorporates the results of math.CO/0506358, math.CO/0507031, and math.CO/0512122, as well as previously unpublished results.
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
This paper discussed the {\it robust alignment} problem, that is, the problem of aligning the goals of algorithms with human preferences. It presented a general roadmap to tackle this issue. Interestingly, this roadmap identifies 5 critical…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
How to get insights from relational data streams in a timely manner is a hot research topic. Data streams can present unique challenges, such as distribution drifts, outliers, emerging classes, and changing features, which have recently…