Tony Johansson

On the insertion time of random walk cuckoo hashing

Cuckoo Hashing is a hashing scheme invented by Pagh and Rodler [12]. It uses d ≥ 2 distinct hash functions to insert items into the hash table. It has been an open question for some time as to the expected time for Random Walk Insertion to add items. We show that if the number of hash functions d = O(1) is sufficiently large, then the expected insertion time is O(1) per item.

On random k‐out subgraphs of large graphs

We consider random sub-graphs of a fixed graph G=(V,E) with large minimum degree. We fix a positive integer k and let Gk be the random sub-graph where each v∈V independently chooses k random neighbors, making kn edges in all. When the minimum degree δ(G)≥(12+ϵ)n,n=|V| then Gk is k-connected w.h.p. for k=O(1); Hamiltonian for ksufficiently large. When δ(G)≥m, then Gk has a cycle of length (1−ϵ)m for k≥kϵ. By w.h.p. we mean that the probability of non-occurrence can be bounded by a function ϕ(n) (or ϕ(m)) where limn→∞ϕ(n)=0.

Minimum Cost Matching in a Random Graph with Random Costs

Let

Permutations in Binary Trees and Split Trees

G_{n,p}

Random Graphs and Algorithms

be the standard Erdős-Renyi-Gilbert random graph and let

The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree.

G_{n,n,p}

The Cover Time of a Biased Random Walk on a Random Cubic Graph.

be the random bipartite graph on

On the insertion time of random walk cuckoo hashing: FRIEZE and JOHANSSON

n+n

Inversions in split trees and conditional Galton-Watson trees

vertices, where each

On edge disjoint spanning trees in a randomly weighted complete graph

e\in [n]^2