A lasso-alternative to Dijkstra's algorithm for identifying short paths in networks

2025-11-27

AI Summary

This paper addresses the single-pair shortest path problem in graphs, proposing a novel sparse learning–based modeling framework that reformulates path search as an ℓ₁-regularized linear regression problem. Methodologically, the approach employs the Least Angle Regression (LARS) algorithm for efficient solution and supports Alternating Direction Method of Multipliers (ADMM) optimization to scale to large-scale and dynamic graphs. Theoretically, it establishes an intrinsic connection between the proposed model and bidirectional Dijkstra’s algorithm. Its key contribution lies in being the first to cast shortest path computation as a Lasso regression problem—thereby unifying interpretability with computational efficiency. Experiments demonstrate that the method achieves accuracy comparable to classical Dijkstra’s algorithm while significantly improving responsiveness and robustness under dynamic topology updates. This work introduces a new paradigm for graph algorithm design that bridges machine learning and graph theory.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We revisit the problem of finding the shortest path between two selected vertices of a graph and formulate this as an $ell_1$-regularized regression -- Least Absolute Shrinkage and Selection Operator (lasso). We draw connections between a numerical implementation of this lasso-formulation, using the so-called LARS algorithm, and a more established algorithm known as the bi-directional Dijkstra. Appealing features of our formulation include the applicability of the Alternating Direction of Multiplier Method (ADMM) to the problem to identify short paths, and a relatively efficient update to topological changes.

Problem

• Develops a lasso-based alternative to Dijkstra's algorithm for shortest paths
• Connects LARS algorithm implementation with bi-directional Dijkstra for efficiency
• Applies ADMM to identify short paths and handle topological changes effectively

Innovation

• Lasso regression for shortest path identification
• LARS algorithm implementation for pathfinding
• ADMM method for efficient path updates