The k-orientability thresholds for Gn, p

  • Authors:
  • Daniel Fernholz;Vijaya Ramachandran

  • Affiliations:
  • -;-

  • Venue:
  • SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2007

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Abstract

We prove that, for k ≥ 2, the k-orientability threshold for the random graph Gn, p coincides with the threshold at which the (k + 1)-core has average degree 2k. The proof involves the analysis of a heuristic algorithm that attempts to find a k-orientation of the random graph. The k-orientation threshold has several applications including offline balanced allocation with a limit of k on maximum bin-size, perfect hashing with a limit of k on maximum chain-length, and concurrent access to parallel memories through redundancy,