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algorithms-optimization / Combinatorial Optimization

Dinitz-Garg-Goemans Conjecture

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.)

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algorithms-optimizationJul 22, 2026Significance 20/100Registry: unreviewed

Dinitz-Garg-Goemans Conjecture

Prior state unknown→disproved

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.)

Source authenticatedDinitz-Garg-Goemans Conjecture →
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Source authenticated

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.)

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