6533b7d5fe1ef96bd1265004
RESEARCH PRODUCT
Optimal Mass Transport on Metric Graphs
Julio RossiJulián ToledoJosé M. Mazónsubject
Voltage graphStrength of a graphDistance-regular graphTheoretical Computer Sciencelaw.inventionPlanar graphMetric k-centerCombinatoricssymbols.namesakelawGraph powerLine graphsymbolsCubic graphSoftwareMathematicsdescription
We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of $p$-Laplacian--type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 | SIAM Journal on Optimization |