1 / 6

Sorting Integers in the RAM Model

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 ). n integers.

job
Download Presentation

Sorting Integers in the RAM Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Sorting (Integers) n integers Input w bits 0 0 1 1 0 - - 0 0 - 0 0 1 1 0 - 0 - 1 - 1 - - 1 0 0 1 1 Output 1 1 0 0 - 1 0 - 1 1 1 1 - 0 - 1 0 0 1 1 1 - 0 0 - 0 - 1 0 0 1 1 - 1 1 - 0 0 - 1 0 - 1 - 0 - Trie Patricia trie (branchingcharctersonly) 0 0 permutation 9 9 7 7 2 2 8 8 10 10 4 4 1 1 6 6 3 3 5 5

  3. ComparisonBasedSorting • Merge sort: von Neumann 1945 • Ford et al. 1959: Lowerbound≥ comparions next scanning next scanning next scanning comparions

  4. Sorting Networks O(n·log2n) size : Batcher 1968 O(n·logn) size : Ajtai, Komlós, Szemerédi 1983; Paterson 1990; Goodrich 2014 Input Output 138 13 13 138 13 13 138 58 55 13 55 58 55 55 58 58 58 55 58 138 55 138 • Original motivated by hardware implementations • Renewedinterestsincedata-oblivious • applications in privacypreservingcomputations • allows for parallel computations on bit-leveland GPU

  5. Time per element Results 2 NEW 1 3 O(1) w log n log2n·loglogn log2+εn 1 2 3

  6. Open Question Time per element Sortingin lineartime for all w? NEW O(1) w log n log2n·loglogn log2+εn

More Related