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

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.