The multiple-orientability thresholds for random hypergraphs

Authors:
Nikolaos Fountoulakis;Megha Khosla;Konstantinos Panagiotou
Affiliations:
Max Planck Institute for Informatics, Saarbrücken, Germany;Max Planck Institute for Informatics, Saarbrücken, Germany;Max Planck Institute for Informatics, Saarbrücken, Germany
Venue:
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Year:
2011

Citing 9
Cited 2

Space Efficient Hash Tables with Worst Case Constant Access Time

STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Cuckoo Hashing

ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Cores in random hypergraphs and Boolean formulas

Random Structures & Algorithms
The cores of random hypergraphs with a given degree sequence

Random Structures & Algorithms
The k-orientability thresholds for Gn, p

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The random graph threshold for k-orientiability and a fast algorithm for optimal multiple-choice allocation

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Load balancing and orientability thresholds for random hypergraphs

Proceedings of the forty-second ACM symposium on Theory of computing
Tight thresholds for cuckoo hashing via XORSAT

ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Orientability of random hypergraphs and the power of multiple choices

ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming

Cuckoo hashing with pages

ESA'11 Proceedings of the 19th European conference on Algorithms
A new approach to the orientation of random hypergraphs

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

A k-uniform hypergraph H = (V, E) is called l-orientable, if there is an assignment of each edge e ε E to one of its vertices v ε e such that no vertex is assigned more than l edges. Let Hn,m,k be a hypergraph, drawn uniformly at random from the set of all k-uniform hypergraphs with n vertices and m edges. In this paper we establish the threshold for the l-orientability of Hn,m,k for all k ≥ 3 and l ≥ 1, i.e., we determine a critical quantity c*k,l such that with probability 1 − o(1) the graph Hn,cn,k has an l-orientation if c c*k,l, but fails doing so if c c*k,l. Our result has various applications including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.