Lasso formulation of the shortest path problem

@article{Dong2020LassoFO,
  title={Lasso formulation of the shortest path problem},
  author={Anqi Dong and Amir Hossein Taghvaei and Tryphon T. Georgiou},
  journal={2020 59th IEEE Conference on Decision and Control (CDC)},
  year={2020},
  pages={402-407}
}
The shortest path problem is formulated as an l1-regularized regression problem, known as lasso. Based on this formulation, a connection is established between Dijkstra’s shortest path algorithm and the least angle regression (LARS) for the lasso problem. Specifically, the solution path of the lasso problem, obtained by varying the regularization parameter from infinity to zero (the regularization path), corresponds to shortest path trees that appear in the bi-directional Dijkstra algorithm. 

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A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.