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. 
View on IEEE
arxiv.org

Figures and Tables from this paper

References

SHOWING 1-10 OF 23 REFERENCES

Least angle regression

A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.

Bi-directional and heuristic search in path problems

This theory shows how a hi- Directional method using the proposed cardinal@ comparison strategy is a priori the best shortest path algorithm within the class of algorithms VGA, a bi-directional extension of the most efficient known uni-directionals shortest path algorithms.

Fast shortest path distance estimation in large networks

This paper proves that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed, and explores theoretical insights to devise a variety of simple methods that scale well in very large networks.

The Lasso Problem and Uniqueness

The LARS algorithm is extended to cover the non-unique case, so that this path algorithm works for any predictor matrix and a simple method is derived for computing the component-wise uncertainty in lasso solutions of any given problem instance, based on linear programming.

Routing of multipoint connections

The author addresses the problem of routing connections in a large-scale packet-switched network supporting multipoint communications. He gives a formal definition of several versions of the…

Network flows - theory, algorithms and applications

In-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models are presented.

Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.

Route Planning in Transportation Networks

It is shown that one can compute driving directions in milliseconds or less even at continental scale, and a variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time.

Regression Shrinkage and Selection via the Lasso

A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.

A note on two problems in connexion with graphs

  • E. Dijkstra
  • Mathematics, Computer Science
    Numerische Mathematik
  • 1959
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.