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Domination is the fastest-growing field within graph theory with a profound diversity and impact in real-world applications, such as the recent breakthrough approach that identifies optimized subsets of proteins enriched with cancer-related…
The degree distribution of a real world network -- the number of links per node -- often follows a power law, with some hubs having many more links than traditional graph generation methods predict. For years, preferential attachment and…
The field of multiobjective evolutionary algorithms (MOEAs) often emphasizes its popularity for optimization problems with conflicting objectives. However, it is still theoretically unknown how MOEAs perform compared with typical approaches…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…
Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…
Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem…
This paper focuses on the exposure to Radio Frequency (RF) Electromagnetic Fields (EMF) and on optimization methods to reduce it. Within the FP7 LEXNET project, an Exposure Index (EI) has been defined that aggregates the essential…
A number of problems in communication systems demand the distributed allocation of network resources in order to provide better services, sampling and distribution methods. The solution to these issues is becoming more challenging due to…
Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
We introduce a minimalistic model based on dynamic node deletion and node duplication with heterodimerisation. The model is intended to capture the essential features of the evolution of protein interaction networks. We derive an exact…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
We consider a wireless network with a set of transmitter-receiver pairs, or links, that share a common channel, and address the problem of emptying finite traffic volume from the transmitters in minimum time. This, so called, minimum-time…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…