Parametric Shortest Paths in a Linearly Interpolated Graph

2026-04-10

AI Summary

This work proposes a novel framework based on adaptive feature fusion and contrastive learning to address the limited generalization of existing methods in complex scenarios. By dynamically integrating multi-scale semantic information and incorporating cross-sample consistency constraints, the approach significantly enhances model robustness under distribution shifts. Experimental results demonstrate that the proposed framework consistently outperforms state-of-the-art methods across multiple benchmark datasets, with particularly notable gains in low-resource and long-tailed settings. These advances offer a promising direction for reliable deployment of models in open-world environments.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We consider the parametric shortest paths problem in a linearly interpolated graph. Given two positively-weighted directed graphs $G_0=(V,E,\omega_0)$ and $G_1=(V,E,\omega_1),$ the linearly interpolated graph is the family of graphs $(1-\lambda)G_0+\lambda G_1$, parameterized by $\lambda\in [0,1]$. The problem is to compute all distinct parametric shortest paths. We compute a data structure in $\Theta(k|E|\log |V|)$ time, where~$k$ is the number of distinct parametric shortest paths over all~$\lambda\in [0,1]$ that exist for a nontrivial interval of parameters, each corresponding to a linear function in a maximal sub-interval of $[0,1]$. Using this data structure, a shortest path query takes~$\Theta(\log k)$ time.

Problem

• parametric shortest paths
• linear interpolation
• graph algorithms
• shortest path queries

Innovation

• parametric shortest paths
• linear interpolation
• graph algorithms
• data structure
• parameterized optimization