Related papers: On Minimal Sets to Destroy the $k$-Core in Random …
We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…
Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…
We consider the rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the…
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of determining a minimum-cost elimination ordering, which we call…
We address the general problem of how best to attack and destroy a network by node removal, given limited or no prior information about the edges. We consider a family of strategies in which nodes are randomly chosen, but not removed.…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
This paper addresses problems on the robust structural design of complex networks. More precisely, we address the problem of deploying the minimum number of dedicated sensors, i.e., those measuring a single state variable, that ensure the…
This paper develops and analyzes optimization models for rapid detection of viruses in large contact networks. In the model, a virus spreads in a stochastic manner over an undirected connected graph, under various assumptions on the spread…
We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…
We study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the…
We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…