Rasmus Pagh

Cuckoo hashing

We present a simple dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. [SIAM J. Comput. 23 (4) (1994) 738-761]. The space usage is similar to that of binary search trees. Besides being conceptually much simpler than previous dynamic dictionaries with worst case constant lookup time, our data structure is interesting in that it does not use perfect hashing, but rather a variant of open addressing where keys can be moved back in their probe sequences. An implementation inspired by our algorithm, but using weaker hash functions, is found to be quite practical. It is competitive with the best known dictionaries having an average case (but no nontrivial worst case) guarantee on lookup time.

Space Efficient Hash Tables With Worst Case Constant Access Time

Abstract We generalize Cuckoo Hashing to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ε)n memory cells, for any constant ε > 0. Assuming uniform hashing, accessing or deleting table entries takes at most d=O (ln (1/ε)) probes and the expected amortized insertion time is constant. This is the first dictionary that has worst case constant access time and expected constant update time, works with (1 + ε)n space, and supports satellite information. Experiments indicate that d = 4 probes suffice for ε ≈ 0.03. We also describe variants of the data structure that allow the use of hash functions that can be evaluated in constant time.

Low Redundancy in Static Dictionaries with Constant Query Time

A static dictionary is a data structure storing subsets of a finite universe U, answering membership queries. We show that on a unit cost RAM with word size

Fast and scalable polynomial kernels via explicit feature maps

\Theta(\log |U|)

Tight thresholds for cuckoo hashing via XORSAT

, a static dictionary for n-element sets with constant worst case query time can be obtained using

Colorful triangle counting and a MapReduce implementation

B+O(\log\log |U|)+o(n)

Simple and space-efficient minimal perfect hash functions

bits of storage, where

Uniform hashing in constant time and linear space

B=\ceiling{\log_2\binom{|U|}{n}}

Uniform Hashing in Constant Time and Optimal Space

is the minimum number of bits needed to represent all n-element subsets of U.

Faster join-projects and sparse matrix multiplications

Approximation of non-linear kernels using random feature mapping has been successfully employed in large-scale data analysis applications, accelerating the training of kernel machines. While previous random feature mappings run in O(ndD) time for