Dinitz-Garg-Goemans Conjecture
Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.
Statement
For single-source unsplittable flow, every fractional flow can be rounded to an unsplittable flow whose cost is no higher than the fractional cost, while each arc's load is exceeded by at most the maximum demand. (The cost version of Goemans' unsplittable-flow conjecture.)
Context
A well-known 1999 conjecture in flow approximation algorithms.
People
Projects
Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.
Interest
Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.
Attempts
No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
Rybin used GPT-5.6 Pro to search for and construct an explicit counterexample: a graph whose fractional flow cost is 58, while every unsplittable flow with capacity violation at most 15 costs at least 60 - so no cost-preserving rounding exists.
Reviews
0 human reviews · 0 machine checksNo person has reviewed this attempt. It has not been checked at all.
Endorsements
0 endorsementsNo one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.
Discussion of this attempt
no comments
Discussion
Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.