Lasso formulation of the shortest path problem
Abstract
The shortest path problem is formulated as an $l_1$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 bidirectional Dijkstra algorithm. Although Dijkstra's algorithm and the LARS formulation provide exact solutions, they become impractical when the size of the graph is exceedingly large. To overcome this issue, the alternating direction method of multipliers (ADMM) is proposed to solve the lasso formulation. The resulting algorithm produces good and fast approximations of the shortest path by sacrificing exactness that may not be absolutely essential in many applications. Numerical experiments are provided to illustrate the performance of the proposed approach.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.09152
 Bibcode:
 2020arXiv200509152D
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Data Structures and Algorithms;
 Mathematics  Statistics Theory;
 Statistics  Applications;
 Statistics  Computation;
 05C38 (Primary) 62J07;
 68R10;
 90C25;
 90C06(Secondary)
 EPrint:
 17 pages