Sorting Integers in the RAM Model Gerth Stølting Brodal Joint work with Djamal Belazzougui and Jesper Sindal Nielsen (to be presented at the 14th Scandinavian.

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Presentation transcript:

Sorting Integers in the RAM Model Gerth Stølting Brodal Joint work with Djamal Belazzougui and Jesper Sindal Nielsen (to be presented at the 14th Scandinavian Workshop on Algorithm Theory) MADALGO Review Meeting, April 28, 2014

Sorting (Integers) Input Output w bits n integers Trie Patricia trie (branching charcters only) permutation

Comparison Based Sorting next scanning

Sorting Networks O(n·log 2 n) size : Batcher 1968 O(n·log n) size : Ajtai, Komlós, Szemerédi 1983; Paterson 1990; Goodrich InputOutput  Original motivated by hardware implementations  Renewed interest since data-oblivious ̶applications in privacy preserving computations ̶allows for parallel computations on bit-level and GPU

Results Bucket sortO(n+2 w ) Radix sort; Hollerith 1887 van Emde Boas 1975 Willard 1983 superlinear space expected Kirkpatrick and Reicsh 1983 Merge sort: von Neumann 1945 comparison based optimal Thorup and Han 2002expected Andersson et al. 1998O(n) NEWO(n) Time per element w log 2 n·loglog nlog 2+ε n O(1) log n NEW

Open Question Sorting in linear time for all w? w log 2 n·loglog nlog 2+ε n O(1) log n NEW Time per element

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