Related papers: Super-linear Lower Bounds for CSP Non-Redundancy v…
Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…
Convolutional neural networks (CNNs) are highly successful for super-resolution (SR) but often require sophisticated architectures with heavy memory cost and computational overhead, significantly restricts their practical deployments on…
In wireless network, the optimization problems generally have complex constraints, and are usually solved via utilizing the traditional optimization methods that have high computational complexity and need to be executed repeatedly with the…
The Feder-Vardi dichotomy conjecture for Constraint Satisfaction Problems (CSPs) with finite templates, confirmed independently by Bulatov and Zhuk, has an extension to certain well-behaved infinite templates due to Bodirsky and Pinsker…
Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certify their robustness. A number of techniques based on convex…
The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…
In the past decade, Deep Neural Networks (DNNs) achieved state-of-the-art performance in a broad range of problems, spanning from object classification and action recognition to smart building and healthcare. The flexibility that makes DNNs…
Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…
We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to…
The Conditional Preference Network (CP-net) graphically represents user's qualitative and conditional preference statements under the ceteris paribus interpretation. The constrained CP-net is an extension of the CP-net, to a set of…
Noncommutative constraint satisfaction problems (NC-CSPs) are higher-dimensional operator extensions of classical CSPs. Despite their significance in quantum information, their approximability remains largely unexplored. A notable example…
Sequential recommendation effectively addresses information overload by modeling users' temporal and sequential interaction patterns. To overcome the limitations of supervision signals, recent approaches have adopted self-supervised…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…
A constraint satisfaction problem (CSP), $\textsf{Max-CSP}(\mathcal{F})$, is specified by a finite set of constraints $\mathcal{F} \subseteq \{[q]^k \to \{0,1\}\}$ for positive integers $q$ and $k$. An instance of the problem on $n$…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis, the convergence of the…
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…