Related papers: Empirical Evaluation of Approximation Algorithms f…
In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real--world instances. The model is more flexible than the semi-random model of Feige and Kilian and…
The paper proves the equivalence of the notions of nondeterministic and deterministic parameter testing for uniform dense hypergraphs of arbitrary order. It generalizes the result previously known only for the case of simple graphs. By a…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
We consider a variant of the densest subgraph problem in networks with single or multiple edge attributes. For example, in a social network, the edge attributes may describe the type of relationship between users, such as friends, family,…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
Given two graphs $G$ and $H$, we investigate for which functions $p=p(n)$ the random graph $G_{n,p}$ (the binomial random graph on $n$ vertices with edge probability $p$) satisfies with probability $1-o(1)$ that every red-blue-coloring of…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve a…
Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…
For a simple graph G = (V, E), a coloring of vertices of G using two colors, say red and blue, is called a quasi neighborhood balanced coloring if, for every vertex of the graph, the number of red neighbors and the number of blue neighbors…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…
We provide a new constant factor approximation algorithm for the (connected) distance-$r$ dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…