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Many patterns in nature exhibit self-similarity: they can be compactly described via self-referential transformations. Said patterns commonly appear in natural and artificial objects, such as molecules, shorelines, galaxies and even images.…
We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible…
In distributed systems, situations often arise where some nodes each holds a collection of tokens, and all nodes collectively need to determine whether all tokens are distinct. For example, if each token represents a logged-in user, the…
In the bin covering problem, the goal is to fill as many bins as possible up to a certain minimal level with a given set of items of different sizes. Online variants, in which the items arrive one after another and have to be packed…
A self-organization of efficient and robust networks is important for a future design of communication or transportation systems, however both characteristics are incompatible in many real networks. Recently, it has been found that the…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
No community detection algorithm can be optimal for all possible networks, thus it is important to identify whether the algorithm is suitable for a given network. We propose a multi-step algorithmic solution scheme for overlapping community…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We…
How to efficiently perform network tomography is a fundamental problem in network management and monitoring. A network tomography task usually consists of applying multiple probing experiments, e.g., across different paths or via different…
Coverage is one of the main quality of service of a wirelessnetwork. $k$-coverage, that is to be covered simultaneously by $k$network nodes, is synonym of reliability and numerous applicationssuch as multiple site MIMO features, or…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
Aiming at improving the efficiency and accuracy of community detection in complex networks, we proposed a new algorithm, which is based on the idea that communities could be detected from subnetworks by comparing the internal and external…
Characterizing the community structure of complex networks is a key challenge in many scientific fields. Very diverse algorithms and methods have been proposed to this end, many working reasonably well in specific situations. However, no…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
In the recent paper \cite{BDT10} we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a "good and fast" packing or…
To better understand the correlation between network topological features and the robustness of network controllability in a general setting, this paper suggests a practical approach to searching for optimal network topologies with given…
In this paper, we investigate the problem of network backbone discovery. In complex systems, a "backbone" takes a central role in carrying out the system functionality and carries the bulk of system traffic. It also both simplifies and…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…