1 / 14

Two Topics in Adaptive Algorithms: Hulls and Strings

Two Topics in Adaptive Algorithms: Hulls and Strings. Robert Fraser University of Waterloo. What to expect. Convex Hulls Adaptive sorting, measures of difficulty Techniques Adaptivity of output sensitive techniques String Matching Online string matching Boyer Moore Horspool technique

jui
Download Presentation

Two Topics in Adaptive Algorithms: Hulls and Strings

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. Two Topics in Adaptive Algorithms: Hulls and Strings Robert Fraser University of Waterloo

  2. What to expect • Convex Hulls • Adaptive sorting, measures of difficulty • Techniques • Adaptivity of output sensitive techniques • String Matching • Online string matching • Boyer Moore Horspool technique • Adaptive string matching

  3. Adaptive Sorting • All kinds of techniques and measures (see Estivill-Castro & Wood, 89) • I love Straight Merge Sort! (Odd-even sms is pretty good too…)

  4. Planar Convex Hulls • Many techniques • Gift wrapping • Graham Scan • Output sensitive • Adaptive (Levcopolous et al., Barbay & Chen) • New adaptive techniques?

  5. Adaptivity of CSY-hull • Ω(n log h) • Add a step CHECKHULL to give adaptivity • Considering performance on a good instance however, you get CUPS • Could also determine difficulty of interior points…

  6. Adaptivity wrt Max! LP sort Quicksort Comparisons LP-odd-even sms Straight mergesort Odd-even sms Max

  7. Adaptivity wrt Runs! LP sort Quicksort LP-odd-even sms Odd-even sms Comparisons Straight mergesort Straight mergesort with reverse! Runs

  8. Busiest slide ever?

  9. New York GIS data 264346 points, 33 on hull sm: 4346700 oesm: 4351874 lpoesm: 6056577 lp: 9408131 gs: 5792637 dis: 263950 max: 207419

  10. String Matching Techniques • Naïve • standard sliding window • θ(n·m) • Linear time • as discussed by KMP • O(n+m) • Expected sublinear • We’ll look at the standard Boyer-Moore Horspool, but there are many! • O(n log m/m +m) expected, O(n·m) worst case

  11. Boyer Moore Horpsool

  12. String Matching with More Jumps • Try to maximize the jumps with Horspool-type searching

  13. Extensions • Uneven distribution of data • 2D string matching • Applications (bioinformatics) • Works best on small alphabets with many repeats

  14. Thanks • Questions? Supported by NSERC and the University of Waterloo

More Related