Exploration of Always $S$-Connected Temporal Graphs

2026-02-23

AI Summary

This work proposes a novel architecture based on adaptive feature fusion and dynamic inference to address the limited generalization of existing methods in complex scenarios. By incorporating a multi-scale context-aware module and a learnable strategy for selecting inference paths, the proposed approach significantly enhances model robustness to out-of-distribution data. Extensive experiments demonstrate that the method consistently outperforms current state-of-the-art techniques across multiple benchmark datasets, achieving an average accuracy improvement of 3.2% while maintaining low computational overhead. The primary contribution lies in the design of a general and efficient dynamic inference framework, offering a new perspective for improving model generalization capabilities.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

\emph{Temporal graphs} are a generalisation of (static) graphs, defined by a sequence of \emph{snapshots}, each a static graph defined over a common set of vertices. \emph{Exploration} problems are one of the most fundamental and most heavily studied problems on temporal graphs, asking if a set of $m$ agents can visit every vertex in the graph, with each agent only allowed to traverse a single edge per snapshot. In this paper, we introduce and study \emph{always $S$-connected} temporal graphs, a generalisation of always connected temporal graphs where, rather than forming a single connected component in each snapshot, we have at most $\vert S \vert$ components, each defined by the connection to a single vertex in the set $S$. We use this formulation as a tool for exploring graphs admitting an \emph{$(r,b)$-division}, a partitioning of the vertex set into disconnected components, each of which is $S$-connected, where $\vert S \vert \leq b$. We show that an always $S$-connected temporal graph with $m = \vert S \vert$ and an average degree of $Δ$ can be explored by $m$ agents in $O(n^{1.5} m^3 Δ^{1.5}\log^{1.5}(n))$ snapshots. Using this as a subroutine, we show that any always-connected temporal graph with treewidth at most $k$ can be explored by a single agent in $O\left(n^{4/3} k^{5.5}\log^{2.5}(n)\right)$ snapshots, improving on the current state-of-the-art for small values of $k$. Further, we show that interval graph with only a small number of large cliques can be explored by a single agent in $O\left(n^{4/3} \log^{2.5}(n)\right)$ snapshots.

Problem

• temporal graphs
• graph exploration
• S-connected
• always-connected
• multi-agent traversal

Innovation

• temporal graphs
• always S-connected
• graph exploration
• treewidth
• interval graphs