Related papers: Replacing spectral techniques for expander ratio, …
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
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…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
In unsplittable network flow problems, certain nodes must satisfy a combinatorial requirement that the incoming arc flows cannot be split or merged when routed through outgoing arcs. This so-called "no-split no-merge" requirement arises in…
Numerical investigation of compressible flows faces two main challenges. In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide…
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…
Solving the non-convex optimal power flow (OPF) problem for large-scale power distribution systems is computationally expensive. An alternative is to solve the relaxed convex problem or linear approximated problem, but these methods lead to…
We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…
Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose…
Graph Partitioning is a critical problem in numerous scientific and engineering domains including social network analysis, VLSI design, and many more. Spectral methods are known to produce quality partitions while minimizing edge cuts for a…
Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the…
The calculation of a three-dimensional underwater acoustic field has always been a key problem in computational ocean acoustics. Traditionally, this solution is usually obtained by directly solving the acoustic Helmholtz equation using a…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…
A numerical algorithm to solve the spectral problem for arbitrary self-adjoint extensions of 1D regular Schroedinger operators is presented. It is shown that the set of all self-adjoint extensions of 1D regular Schroedinger operators is in…
Message Passing Graph Neural Networks are known to suffer from two problems that are sometimes believed to be diametrically opposed: over-squashing and over-smoothing. The former results from topological bottlenecks that hamper the…
With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation.…
We investigate the perturbation dynamics in a supersonic shear layer using a combination of large-eddy simulations (LES) and linear-operator-based input-output analysis. The flow consists of two streams-a main stream (Mach 1.23) and a…
Orthogonality constrained optimization is widely used in applications from science and engineering. Due to the nonconvex orthogonality constraints, many numerical algorithms often can hardly achieve the global optimality. We aim at…
The load-flow equations are the main tool to operate and plan electrical networks. For transmission or distribution networks these equations can be simplified into a linear system involving the graph Laplacian and the power input vector. We…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…