The rapid evolution of cellular networks has made them a critical infrastructure for modern society, but it has also led to quickly increasing energy consumption. Open Radio Access Network (O-RAN), with its disaggregated architecture, offers significant potential for improving energy efficiency (EE) in next-generation networks. This survey presents a comprehensive review of state-of-the-art O-RAN energy efficiency research, structured around three key dimensions: energy measurement, energy modeling, and energy optimization. We examine both software- and hardware-based measurement techniques, highlighting their strengths, limitations, and applicability on different network functions. The survey then categorizes existing energy consumption models into theoretical and empirical approaches, with a discussion of their methodologies and constraints. Finally, we explore energy optimization strategies defined by O-RAN specifications and beyond, revealing diverse technical directions in academia and industry. The survey also highlights emerging research challenges, including the lack of high-fidelity and generic datasets, the need for standardized evaluation frameworks and methodologies, and the impact of continuous O-RAN evolution on the validity of existing studies. Overall, this work aims to serve as a foundational reference for researchers and engineers to build sustainable and energy-aware O-RAN networks.

In this paper, we address the problem of fast computation and optimization of opinion-based quantities in the Friedkin–Johnsen (FJ) model. We first introduce the concept of partial rooted forests and present an efficient algorithm for computing these quantities using this method. Furthermore, we study two optimization problems in the FJ model: the Opinion Minimization Problem and the Polarization and Disagreement Minimization Problem. For both problems, we propose fast algorithms based on partial rooted forest sampling. Our methods reduce the time complexity from linear to sublinear. Extensive experiments on real-world networks demonstrate that our algorithms are both accurate and efficient, outperforming state-of-the-art methods and scaling effectively to large-scale networks.

Centrality measures are essential for identifying important nodes and edges in networks. In this paper, we focus on two forest-based centrality measures on undirected graphs: forest node centrality (FNC) and forest edge centrality (FEC), which capture the influence of nodes and edges through their participation in spanning forests. Both centrality measures can be represented using entries of the forest matrix. To address the challenge of computing the two measures on large networks, we propose two scalable algorithms from different perspectives. The first algorithm IFGN combines two variance reduction techniques to approximate the entries of the forest matrix, applicable to both FNC and FEC.The second algorithm FECE incorporates a new physical interpretation of FEC, allowing for a better overall estimation. We provide error guarantees for both algorithms and demonstrate their efficiency and effectiveness through extensive experiments on various real-world networks.

O-RAN (Open Radio Access Network) multivendor integration, despite its promise of a diverse 5G ecosystem, faces compatibility challenges such as vendor-specific implementations. We propose WA-RAN, a novel framework that leverages WebAssembly (Wasm) to enhance interoperability and flexibility within the O-RAN architecture. Using Wasm plugins, WA-RAN addresses the complexities of integrating multivendor equipment, enables components update on the fly, and facilitates the introduction of new features. Additionally, it offers platform and language agnosticism along with enhanced security via sandboxing. We demonstrate the design of WA-RAN through two use cases in 5G: a slice scheduler and a near-Real-Time RAN Intelligent Controller (near-RT RIC). Our implementation and evaluation show WA-RAN potential to safely overcome O-RAN integration challenges, providing a promising path to versatile 5G networks.

The forest matrix plays a crucial role in network science, opinion dynamics, and machine learning, offering deep insights into the structure of and dynamics on networks. In this paper, we study the problem of querying entries of the forest matrix in evolving graphs, which more accurately represent the dynamic nature of real-world networks compared to static graphs. To address the unique challenges posed by evolving graphs, we first introduce two approximation algorithms, SFQ and SFQPlus, for static graphs. SFQ employs a probabilistic interpretation of the forest matrix, while SFQPlus incorporates a novel variance reduction technique and is theoretically proven to offer enhanced accuracy. Based on these two algorithms, we further devise two dynamic algorithms centered around efficiently maintaining a list of spanning converging forests. This approach ensures O(1) runtime complexity for updates, including edge additions and deletions, as well as for querying matrix elements, and provides an unbiased estimation of forest matrix entries. Finally, through extensive experiments on various real-world networks, we demonstrate the efficiency and effectiveness of our algorithms. Particularly, our algorithms are scalable to massive graphs with more than forty million nodes.

The forest matrix of a graph, particularly its diagonal elements, has far-reaching implications in network science and machine learning. The state-of-the-art algorithms for the diagonal of forest matrix computation are based on the fast Laplacian solver. However, these algorithms encounter limitations when applied to digraphs due to the incapacity of the Laplacian solver. To overcome the issue, in this paper, we propose three novel sampling-based algorithms:SCF,SCFV,and SCFV+. Our first algorithm SCF leverages a probability interpretation of the diagonal of the forest matrix and utilizes an extension of Wilson's algorithm to sample spanning converging forests. To reduce the variance in the forest sampling, we develop two novel variance-reduced techniques. The first technique, leading to the proposal of the SCFV algorithm, is inspired by opinion dynamics in graphs and applies matrix-vector iteration to the spanning forest sampling. While SCFV achieves reduced variance compared to SCF, the cross-product term in its variance expression can be complex and potentially large in certain graphs. Therefore, we develop another technique, leading to a new iteration equation and the SCFV+ algorithm. SCFV+ achieves further reduced variance without the cross-product term in the variance of SCFV. We prove that SCFV+ can achieve a relative error guarantee with high probability and maintain a linear time complexity relative to the number of nodes in the graph, presenting a superior theoretical result compared to state-of-the-art algorithms. Finally, we conduct extensive experiments on various real-world networks, showing that our algorithms achieve better estimation accuracy and are more time-efficient than the state-of-the-art algorithms. Particularly, our algorithms are scalable to massive graphs with more than twenty million nodes in both undirected and directed graphs.

A signed graph offers richer information than an unsigned graph, since it describes both collaborative and competitive relationships in social networks. In this paper, we study opinion dynamics on a signed graph, based on the Friedkin-Johnsen model. We first interpret the equilibrium opinion in terms of a defined random walk on an augmented signed graph, by representing the equilibrium opinion of every node as a combination of all nodes’ internal opinions, with the coefficient of the internal opinion for each node being the difference of two absorbing probabilities. We then quantify some relevant social phenomena and express them in terms of the$\ell _{2}$norms of vectors. We also design a nearly-linear time signed Laplacian solver for assessing these quantities, by establishing a connection between the absorbing probability of random walks on a signed graph and that on an associated unsigned graph. We further study the opinion optimization problem by changing the initial opinions of a fixed number of nodes, which can be optimally solved in cubic time. We provide a nearly-linear time algorithm with an error guarantee to approximately solve the problem. Finally, we execute extensive experiments on sixteen real-life signed networks, which show that both of our algorithms are effective and efficient, and are scalable to massive graphs with over 20 million nodes.

Shifting social opinions has far-reaching implications in various aspects, such as public health campaigns, product marketing, and political candidates. In this paper, we study a problem of opinion optimization based on the popular Friedkin-Johnsen (FJ) model for opinion dynamics in an unweighted directed social network with n nodes and m edges. In the FJ model, the internal opinion of every node lies in the closed interval [0, 1], with 0 and 1 being polar opposites of opinions about a certain issue. Concretely, we focus on the problem of selecting a small number of k

In this paper, we propose a new method of visualizing hierarchical time-series data. We use the hyperbolic tree to visualize the hierarchical structure. The hyperbolic tree can visualize large hierarchical structure. It allocates more space for the nodes of our concern, with the entire hierarchical structure being displayed at the same time. We utilize the time disc, which is similar to the spiral, to display the time-series data. Unlike traditional bar charts and line graphs, the time disc is suited to visualizing large data set and supporting much better the identification of features in the data, such as periodicity and trends. The method can easily display large hierarchical structure and time-series data. We visualize the time series data of each child node by selecting the parent node in the hyperbolic tree, and then observe the similarities and differences between the nodes and the trends of the thing. We applied this method to the urban air quality data visualization and achieved good results.