Tight Bounds for Gomory-Hu-like Cut Counting

@article{Chitnis2016TightBF,
  title={Tight Bounds for Gomory-Hu-like Cut Counting},
  author={Rajesh Hemant Chitnis and Lior Kamma and Robert Krauthgamer},
  journal={ArXiv},
  year={2016},
  volume={abs/1511.08647}
}
  • Rajesh Hemant Chitnis, Lior Kamma, Robert Krauthgamer
  • Published in WG 2016
  • Mathematics, Computer Science
  • ArXiv
  • By a classical result of Gomory and Hu (1961), in every edge-weighted graph $G=(V,E,w)$, the minimum $st$-cut values, when ranging over all $s,t\in V$, take at most $|V|-1$ distinct values. That is, these $\binom{|V|}{2}$ instances exhibit redundancy factor $\Omega(|V|)$. They further showed how to construct from $G$ a tree $(V,E',w')$ that stores all minimum $st$-cut values. Motivated by this result, we obtain tight bounds for the redundancy factor of several generalizations of the minimum $st… CONTINUE READING
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