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Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
We develop an algorithm for systematic design of a large artificial neural network using a progression property. We find that some non-linear functions, such as the rectifier linear unit and its derivatives, hold the property. The…
Dominating sets in graphs are often used to model some monitoring of the graph: guards are posted on the vertices of the dominating set, and they can thus react to attacks occurring on the unguarded vertices by moving there (yielding a new…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
We present new greedy and beam search heuristic methods to find small-size $k$-dominating sets in graphs. The methods are inspired by a new problem formulation which explicitly highlights a certain structure of the problem. An empirical…
For a positive integer $r$, a distance-$r$ independent set in an undirected graph $G$ is a set $I\subseteq V(G)$ of vertices pairwise at distance greater than $r$, while a distance-$r$ dominating set is a set $D\subseteq V(G)$ such that…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…
In this paper, we consider a randomized greedy algorithm for independent sets in $r$-uniform $d$-regular hypergraphs $G$ on $n$ vertices with girth $g$. By analyzing the expected size of the independent sets generated by this algorithm, we…
Numerous problems consisting in identifying vertices in graphs using distances are useful in domains such as network verification and graph isomorphism. Unifying them into a meta-problem may be of main interest. We introduce here a…
This research paper addresses the stability of search algorithms in complex networks when dealing with incomplete information or uncertainty. We propose a theoretical model to investigate whether a global search algorithm with incomplete…
We present two new combinatorial tools for the design of parameterized algorithms. The first is a simple linear time randomized algorithm that given as input a $d$-degenerate graph $G$ and an integer $k$, outputs an independent set $Y$,…
A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This…
The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…
The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large…
Let $r\ge 3$ be a fixed constant and let $ {\mathcal H}$ be an $r$-uniform, $D$-regular hypergraph on $N$ vertices. Assume further that $ D > N^\varepsilon $ for some $ \varepsilon>0 $. Consider the random greedy algorithm for forming an…
Let G be a graph. The independence-domination number is the maximum over all independent sets I in G of the minimal number of vertices needed to dominate I. In this paper we investigate the computational complexity of independence…