Network flow in the nth-dimension! Basically a higher dimensional generalization of minimum cost network flow.
First install like this:
npm install ndflow
Then use it as follows:
require("ndflow")( [[0,1,2], [1,2,3]], //Simplicial complex [1, 1], //Capacities [[0,1], [1,3], [3,2], [2,0]], //Boundary circulation [1,1,1,1], //Boundary weights [1,1]) //Cost function
require("ndflow")(cells, capacities, boundary_cells, boundary_weights, cost)
Solves for the flow from the boundary cells that minimizes the cost. This is the same thing as solving the linear program:
Minimize cost(flow) Subject to D(flow) = boundary_cells * boundary_weights 0 <= flow <= capacities
In the case where the cell complex is one dimensional, this is the same as solving minimum cost network flow for a given capacity. Binary searching on the scale of the capacities lets one compute a maximum/min-cost flow.
(c) 2013 Mikola Lysenko. BSD License