相关论文: Exploring two concepts: branch decomposition and w…
We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…
A median graph is a connected graph, such that for any three vertices $u,v,w$ there is exactly one vertex $x$ that lies simultaneously on a shortest $(u,v)$-path, a shortest $(v,w)$-path and a shortest $(w,u)$-path. Examples of median…
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…
Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…
Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves…
The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…
Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem…
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
The future of main memory appears to lie in the direction of new technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of latency, bandwidth, and energy.…
Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In…