相关论文: Optimization methods for frame conditioning and ap…

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…

The Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a…

Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks,…

We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in…

This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph Laplacian. A bound is derived on the energy norm of the…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

We suggest modified bi-level approach for finding the best stacking sequence of laminated composite structures subject to mechanical, blending and manufacturing constraints. We propose to use both the number of plies laid up at predefined…

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…

We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number…

In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an…

Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space.…

We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee, Meeks and Pettersson (Stat. Comput. 2021) recently demonstrated that improved inference for areal unit count data can be achieved by…

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive…

Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting,…

Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…

We study a Bayesian approach to estimating a smooth function in the context of regression or classification problems on large graphs. We derive theoretical results that show how asymptotically optimal Bayesian regularization can be achieved…