Related papers: Optimal Graph Stretching for Distributed Averaging
Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Consider the setting where each vertex of a graph has a function, and communications can only occur between vertices connected by an edge. We wish to minimize the sum of these functions. For the case when each function is the sum of a…
We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
The diameter of a graph is one if its most important parameters, being used in many real-word applications. In particular, the diameter dictates how fast information can spread throughout data and communication networks. Thus, it is a…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Connectivity is a central notion of graph theory and plays an important role in graph algorithm design and applications. With emerging new applications in networks, a new type of graph connectivity problem has been getting more…
We consider network structures that optimize the $\mathcal{H}_2$ norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
We consider the problem of accelerating distributed optimization in multi-agent networks by sequentially adding edges. Specifically, we extend the distributed dual averaging (DDA) subgradient algorithm to evolving networks of growing…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Convexification techniques have gained increasing interest over the past decades. In this work, we apply a recently developed convexification technique for fractional programs by He, Liu and Tawarmalani (2024) to the problem of determining…
The in-memory graph layout or organization has a considerable impact on the time and energy efficiency of distributed memory graph computations. It affects memory locality, inter-task load balance, communication time, and overall memory…
We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of…