Dinitz–Garg–Goemans conjecture

In combinatorial optimization, the Dinitz–Garg–Goemans conjecture, also called Goemans' conjecture or the cost conjecture, is a statement about single-source unsplittable flows. It concerns the problem of converting a fractional flow, which may split each terminal's demand across several paths, into an unsplittable one, which routes each demand along a single path, without straying too far from the original. The conjecture asserts that given any fractional flow and any assignment of costs to the arcs, there is an unsplittable flow that exceeds the fractional flow on each arc by at most the maximum demand while costing no more than the fractional flow overall.