The line flow solvers solves the following problem:
Given a graph and a set of lines, assign lines to edges, such that the overall edge cost is minimized.
Input:
- A directed graph
- A cost vector for each edge
- A set of lines 1..L
- Tuples of edge/line combinations that fix lines to edges
- A set of edges where only one line can be assigned to
Goal: Minimize the sume of cost of all line/edge tuples
Subject to:
- Certain line/edge tuples are fixed
- Only one line can be assigned to certain edges
- If a line enters a node, then a line must also leave the node
Output:
- An assignment of lines to edges