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We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
This paper investigates the impact of addition/removal of edges in a complex networked control system, for the purposes of improving its controllability, system performances or robustness to external disturbances. The transfer function…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done…
Finding the shortest path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has been successfully attempted on this problem, most of which is limited to static graphs.…
Graph Neural Networks (GNNs) have proven to be powerful in many graph-based applications. However, they fail to generalize well under heterophilic setups, where neighbor nodes have different labels. To address this challenge, we employ a…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
Computing distances and finding shortest paths in massive real-world networks is a fundamental algorithmic task in network analysis. There are two main approaches to solving this task. On one hand are traversal-based algorithms like…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known…
Smart city has been consider the wave of the future and the route recommendation in networks is a fundamental problem in it. Most existing approaches for the shortest route problem consider that there is only one kind of cost in networks.…
The online weighted matching problem is a fundamental problem in machine learning due to its numerous applications. Despite many efforts in this area, existing algorithms are either too slow or don't take $\mathrm{deadline}$ (the longest…
In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…