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Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step,…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we…
Let $G$ be a planar graph and $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a "token" on each vertex of $I_s$ and seek to move all tokens to $I_t$, by repeated "token jumping", removing a single token from…
A maximal independent set in a graph $G$ is an independent set that cannot be extended to a larger independent set by adding any vertex from $G$. This paper investigates the problem of determining the maximum number of maximal independent…
This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that…
In the deeply interconnected world we live in, pieces of information link domains all around us. As graph databases embrace effectively relationships among data and allow processing and querying these connections efficiently, they are…
One of the prominent areas of research in graph theory is the degree-diameter problem, in which we seek to determine how many vertices a graph may have when constrained to a given degree and diameter. Different variants of this problem are…
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…
In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
The recent work ``Combinatorial Optimization with Physics-Inspired Graph Neural Networks'' [Nat Mach Intell 4 (2022) 367] introduces a physics-inspired unsupervised Graph Neural Network (GNN) to solve combinatorial optimization problems on…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…
An independent vertex set of a graph is a set of vertices of the graph in which no two vertices are adjacent, and a maximal independent set is one that is not a proper subset of any other independent set. In this paper we count the number…
In single channel wireless networks, concurrent transmission at different links may interfere with each other. To improve system throughput, a scheduling algorithm is necessary to choose a subset of links at each time slot for data…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Model repair is an essential topic in model-driven engineering. Since models are suitably formalized as graph-like structures, we consider the problem of rule-based graph repair: Given a rule set and a graph constraint, try to construct a…