Random Structures & Algorithms
Space Efficient Hash Tables with Worst Case Constant Access Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Cuckoo hashing: further analysis
Information Processing Letters
Cores in random hypergraphs and Boolean formulas
Random Structures & Algorithms
Avoidance of a giant component in half the edge set of a random graph
Random Structures & Algorithms
The cores of random hypergraphs with a given degree sequence
Random Structures & Algorithms
A phase transition for avoiding a giant component
Random Structures & Algorithms
Balanced allocation and dictionaries with tightly packed constant size bins
Theoretical Computer Science
The k-orientability thresholds for Gn, p
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Why simple hash functions work: exploiting the entropy in a data stream
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorica
On risks of using cuckoo hashing with simple universal hash classes
SODA '09 Proceedings of the twentieth 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
Tight thresholds for cuckoo hashing via XORSAT
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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
The multiple-orientability thresholds for random hypergraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bipartite graph structures for efficient balancing of heterogeneous loads
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Sharp load thresholds for cuckoo hashing
Random Structures & Algorithms
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A hypergraph H = (V,E) is called s-orientable, if there is an assignment of each edge e ∈ E to one of its vertices v ∈ e such that no vertex is assigned more than s 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 1-orientability of Hn,m,k for all k ≥ 3, i.e., we determine a critical quantity ck* such that with probability 1 - o(1) the graph Hn,cn,k has a 1-orientation if c ck*, but fails doing so if c ck*. We present two applications of this result that involve the paradigm of multiple choices. First, we show how it implies sharp load thresholds for cuckoo hash tables, where each element chooses k out of n locations. Particularly, for each k ≥ 3 we prove that with probability 1 - o(1) the maximum number of elements that can be hashed is (1 - o(1))ck*n, and more items prevent the successful allocation. Second, we study random graph processes, where in each step we have the choice among any edge connecting k random vertices. Here we show the existence of a phase transition for avoiding a giant connected component, and quantify precisely the dependence on k.