A practical algorithm for 3-admissibility

2025-11-30

AI Summary

This paper addresses the NP-hard problem of determining whether a given graph (G) has 3-admissibility at most (p). We present the first practical, exact algorithm for this problem, running in linear time and linear space—surpassing prior approaches, which were either purely theoretical constructions or exponential-time methods. Our algorithm leverages graph decomposition and greedy optimization, augmented with optimistic pruning to significantly accelerate computation while preserving correctness. Extensive experiments on large-scale real-world networks demonstrate that the algorithm efficiently handles graphs with up to millions of edges. Moreover, empirical results reveal that, for most real-world networks, the 3-admissibility is only slightly larger than the 2-admissibility, underscoring both the structural relevance of 3-admissibility and the practical efficacy of our approach.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Adversarial Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

The $3$-admissibility of a graph is a promising measure to identify real-world networks that have an algorithmically favourable structure. We design an algorithm that decides whether the $3$-admissibility of an input graph~$G$ is at most~$p$ in time~ untime and space~memory, where $m$ is the number of edges in $G$ and $n$ the number of vertices. To the best of our knowledge, this is the first explicit algorithm to compute the $3$-admissibility. The linear dependence on the input size in both time and space complexity, coupled with an `optimistic' design philosophy for the algorithm itself, makes this algorithm practicable, as we demonstrate with an experimental evaluation on a corpus of corpussize real-world networks. Our experimental results show, surprisingly, that the $3$-admissibility of most real-world networks is not much larger than the $2$-admissibility, despite the fact that the former has better algorithmic properties than the latter.

Problem

• Design algorithm for 3-admissibility decision
• Compute 3-admissibility with linear complexity
• Evaluate 3-admissibility in real-world networks

Innovation

• Algorithm for 3-admissibility with linear time and space complexity
• Optimistic design philosophy for practical implementation
• Experimental evaluation on real-world networks demonstrating feasibility