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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…
In the k-partition problem (k-PP), one is given an edge-weighted undirected graph, and one must partition the node set into at most k subsets, in order to minimise (or maximise) the total weight of the edges that have their end-nodes in the…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Given a graph with edge costs, the {\em power} of a node is themaximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following…
Thesis Statement: Cost-effective switching and spectrum utilization efficiency have become critical design considerations in optical networks. This dissertation provides in-depth exploration of these important aspects, and proposes…
The degree/diameter problem for mixed graphs asks for the largest possible order of a mixed graph with given diameter and degree parameters. Similarly the \emph{degree/geodecity} problem concerns the smallest order of a $k$-geodetic mixed…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph…
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…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We initiate the study of degree-bounded network design problems in the online setting. The degree-bounded Steiner tree problem { which asks for a subgraph with minimum degree that connects a given set of vertices { is perhaps one of the…
This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional…
In single channel wireless networks, concurrent transmission at different links may interfere with each other. To improve system throughput, a scheduling algorithm is necessary to choose a subset of links at each time slot for data…
Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a…
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…
Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max…
A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a…
In this paper, we initiate the study of the vertex coloring problem of a graph in the semi streaming model. In this model, the input graph is defined by a stream of edges, arriving in adversarial order and any algorithm must process the…
The general communication tree embedding problem is the problem of mapping a set of communicating terminals, represented by a graph G, into the set of vertices of some physical network represented by a tree T. In the case where the vertices…