Related papers: Edge expansion of a graph: SDP-based computational…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and…
The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem…
We study the following two fixed-cardinality optimization problems (a maximization and a minimization variant). For a fixed $\alpha$ between zero and one we are given a graph and two numbers $k \in \mathbb{N}$ and $t \in \mathbb{Q}$. The…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
The performance of distributed averaging depends heavily on the underlying topology. In various fields, including compressed sensing, multi-party computation, and abstract graph theory, graphs may be expected to be free of short cycles,…
The visualization of any graph plays important role in various aspects, such as graph drawing software. Complex systems (like large databases or networks) that have a graph structure should be properly visualized in order to avoid…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
In this paper, we introduce a new model for sublinear algorithms called \emph{dynamic sketching}. In this model, the underlying data is partitioned into a large \emph{static} part and a small \emph{dynamic} part and the goal is to compute a…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
In the graph balancing problem the goal is to orient a weighted undirected graph to minimize the maximum weighted in-degree. This special case of makespan minimization is NP-hard to approximate to a factor better than 3/2 even when there…
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…
Vector graphics includes both filled and stroked paths as the main primitives. While there are many techniques for rendering filled paths on GPU, stroked paths have proved more elusive. This paper presents a technique for performing stroke…
The multicut problem is an NP-hard combinatorial optimization problem with diverse applications in fields such as bioinformatics, data mining and computer vision. Graph neural networks have been defined for the multicut problem but can be…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…