相关论文: Lipschitz Continuous Algorithms for Covering Probl…

Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable…

Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…

In many real-world applications, it is undesirable to drastically change the problem solution after a small perturbation in the input, as unstable outputs can lead to costly transaction fees, privacy and security concerns, reduced user…

A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…

Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…

A typical goal of research in combinatorial optimization is to come up with fast algorithms that find optimal solutions to a computational problem. The process that takes a real-world problem and extracts a clean mathematical abstraction of…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

Recent research has examined algorithms to minimize robots' resource footprints. The class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods for reducing their space…

What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically. As lossless state compression…

Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter…

The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…

In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…

Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

A hitting set for a collection of sets is a set that has a non-empty intersection with each set in the collection; the hitting set problem is to find a hitting set of minimum cardinality. Motivated by instances of the hitting set problem…

Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…