top of page
스크린샷 2021-05-09 오후 2.40.46.png
스크린샷 2021-05-09 오후 2.40.21.png

Using Local Indicators to Unitary and Balanced Transport Problems with Concave Costs

(Applied Mathematics)

J. Delon., J. Salomon., A. Sobolevskii.

Revised by S. Yoon. under supervision of Dr. J. Salomon.

Optimal transport problems consist of transferring mass from a series of supplies to demands. Within this paper, we focus on a specific instance of such problems, which is the unitary and balanced transport problem with concave cost. Unitary means that there is no mass left after the transportation is finishes; balanced means that there is an equal number of supplies and demands. On a one dimensional case of such problems, that is, such problem on a line, we define structures called chains. Using concavity of the cost function, we seek to define a local indicator on a chain, which will then be used to deduce the global optimum transport plan. 

The algorithm allows a deeper understanding of optimal transport problems on a line. Although the time complexity of the algorithm has not been so well-understood, the prospect for local matching indicators to be used as a solution for the unsolved optimal transport problem in two dimensions or 1.5 dimensions (i.e. a graph) still remains. 

bottom of page