Related papers: A Generalized Matching Reconfiguration Problem
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optimal cubature schemes and rational optimization. Using the…
Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…
The main goal in distributed symmetry-breaking is to understand the locality of problems; i.e., the radius of the neighborhood that a node needs to explore in order to arrive at its part of a global solution. In this work, we study the…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
The exact matching problem is a constrained variant of the maximum matching problem: given a graph with each edge having a weight $0$ or $1$ and an integer $k$, the goal is to find a perfect matching of weight exactly $k$. Mulmuley,…
In this work, we study the Induced Matching problem: Given an undirected graph $G$ and an integer $\ell$, is there an induced matching $M$ of size at least $\ell$? An edge subset $M$ is an induced matching in $G$ if $M$ is a matching such…
Group distributionally robust optimization (GDRO) aims to develop models that perform well across $m$ distributions simultaneously. Existing GDRO algorithms can only process a fixed number of samples per iteration, either 1 or $m$, and…
Policy optimization, which finds the desired policy by maximizing value functions via optimization techniques, lies at the heart of reinforcement learning (RL). In addition to value maximization, other practical considerations arise as…
Regular expression matching is essential for many applications, such as finding patterns in text, exploring substrings in large DNA sequences, or lexical analysis. However, sequential regular expression matching may be time-prohibitive for…
We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…
The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…