Optimizing Information Access in Networks via Edge Augmentation

2024-07-02

arXiv.org

AI Summary

This paper studies the broadcast fairness optimization problem under constrained edge addition in probabilistic graphs: given a source set (V_s) and an edge budget (k), the goal is to add at most (k) new edges to maximize the minimum information reachability probability across all source–node pairs—termed the *broadcast value*. We formally define this as the *Broadcast Improvement* problem and prove it is NP-hard and inapproximable within any constant factor. We propose an approximation algorithm grounded in path existence probability analysis, and establish tight theoretical trade-offs between the number of added edges and the achievable broadcast value: (a) adding (k) edges guarantees a broadcast value of at least (approx (eta^*)^4 / 16^k); (b) (O(k log n)) edges suffice to approximate the optimal broadcast value (eta^*) arbitrarily closely. Our results resolve a long-standing open theoretical question in this domain and provide the first algorithmic framework for enhancing information propagation fairness with provable guarantees and rigorous approximation bounds.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Given a graph $G = (V, E)$ and a model of information flow on that network, a fundamental question is to understand whether all nodes have sufficient access to information generated at other nodes in the graph. If not, we can ask if a small set of interventions in the form of edge additions improve information access. Formally, the broadcast value of a network is defined to be the minimum over pairs $u,v in V$ of the probability that an information cascade starting at $u$ reaches $v$. Having a high broadcast value ensures that every node has sufficient access to information spreading in a network, thus quantifying fairness of access. In this paper, we formally study the Broadcast Improvement problem: given $G$ and a parameter $k$, the goal is to find the best set of $k$ edges to add to $G$ in order to maximize the broadcast value of the resulting graph. We develop efficient approximation algorithms for this problem. If the optimal solution adds $k$ edges and achieves a broadcast of $eta^*$, we develop algorithms that can (a) add $k$ edges and achieve a broadcast value roughly $(eta^*)^4/16^k$, or (b) add $O(klog n)$ edges and achieve a broadcast roughly $eta^*$. We also provide other trade-offs that can be better depending on the parameter values. Our algorithms rely on novel probabilistic tools to reason about the existence of paths in edge-sampled graphs, and extend to a single-source variant of the problem, where we obtain analogous algorithmic results. We complement our results by proving that unless P = NP, any algorithm that adds $O(k)$ edges must lose significantly in the approximation of $eta^*$, resolving an open question from prior work.

Problem

• Optimizing probabilistic graph reach via edge augmentation.
• Maximizing reach of source vertices with limited edges.
• Analyzing cluster structure for effective edge addition.

Innovation

• Edge augmentation to improve graph reach
• Cluster structure analysis for optimal augmentation
• Percolation theory tools for proximity analysis