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#### Space Efficient Hash Tables With Worst Case Constant Access Time

##### MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44436

Fotakis,  Dimitris
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45344

Sanders,  Peter
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45532

Spirakis,  Paul
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Citation

Fotakis, D., Pagh, R., Sanders, P., & Spirakis, P. (2005). Space Efficient Hash Tables With Worst Case Constant Access Time. Theory of Computing Systems, 38, 229-248.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-27B9-3
##### Abstract
We generalize Cuckoo Hashing to \emph{$d$-ary Cuckoo Hashing} and show how this yields a simple hash table data structure that stores $n$ elements in $(1+\e)\,n$ memory cells, for any constant $\e > 0$. Assuming uniform hashing, accessing or deleting table entries takes at most $d=\Oh{\ln\frac{1}{\e}}$ 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 $(1+\e)\,n$ space, and supports satellite information. Experiments indicate that $d=4$ probes suffice for $\e\approx 0.03$. We also describe variants of the data structure that allow the use of hash functions that can be evaluated in constant time.