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

TL;DR

This paper introduces a novel approach to shortest path problems in networks by formulating it as an $ ext{L}_1$-regularized regression problem, leveraging lasso techniques and ADMM, offering an alternative to traditional algorithms like Dijkstra.

Contribution

The paper presents a new lasso-based formulation for shortest path identification and connects it with existing algorithms, enabling efficient updates and broader applicability.

Findings

Lasso formulation effectively identifies shortest paths.

ADMM facilitates efficient computation and updates.

Connections established between lasso methods and Dijkstra's algorithm.

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.