4421 eng reportzib 0 -- 2014-02-18 -- We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We show that the concept of metric inequalities to characterize capacities that support a multi-commodity flow can be generalized to deal with direct connections. 1438-0064 urn:nbn:de:0297-zib-44219 Ralf Borndörfer Marika Karbstein Marika Karbstein 14-04 eng uncontrolled metric inequalities eng uncontrolled direct connection eng uncontrolled multi-commodity flow problem Integer programming Combinatorial optimization Mathematical Optimization Mathematics of Transportation and Logistics Borndörfer, Ralf MATHEON-B15 Applied Optimization https://opus4.kobv.de/opus4-zib/files/4421/ZR14_04.pdf