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The shortest path problem is formulated as an $l_1$-regularized regressionproblem, known as lasso. Based on this formulation, a connection is establishedbetween Dijkstra's shortest path algorithm and the least angle regression(LARS) for the lasso problem. Specifically, the solution path of the lassoproblem, obtained by varying the regularization parameter from infinity to zero(the regularization path), corresponds to shortest path trees that appear inthe bi-directional Dijkstra algorithm. Although Dijkstra's algorithm and theLARS formulation provide exact solutions, they become impractical when the sizeof the graph is exceedingly large. To overcome this issue, the alternatingdirection method of multipliers (ADMM) is proposed to solve the lassoformulation. The resulting algorithm produces good and fast approximations ofthe shortest path by sacrificing exactness that may not be absolutely essentialin many applications. Numerical experiments are provided to illustrate theperformance of the proposed approach.

Lasso formulation of the shortest path problem