Related papers: Approximating Flexible Graph Connectivity via R\"a…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…
Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…
Bobkov, Houdr\'e, and the last author [2000] introduced a Poincar\'e-type functional parameter, $\lambda_\infty$, of a graph and related it to connectivity of the graph via Cheeger-type inequalities. A work by the second author,…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
The current surge of interest in graph-based data models mirrors the usage of increasingly complex reachability queries, as witnessed by recent analytical studies on real-world graph query logs. Despite the maturity of graph DBMS…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
Interconnected complex systems usually undergo disruptions due to internal uncertainties and external negative impacts such as those caused by harsh operating environments or regional natural disaster events. To maintain the operation of…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
Graph convolutional networks (GCNs) have gained popularity due to high performance achievable on several downstream tasks including node classification. Several architectural variants of these networks have been proposed and investigated…
This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected sub-networks…
Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…