Group project 1 from the course Advanced Algorithms

• Part One

  A) "Mom bought me a new computer"

  Implement the following pattern matching algorithms: Brute-force, Sunday, KMP, FSM, Rabin-Karp, Gusfield Z. Compare their running times using chapters of a book, with a small (few words or a sentence) and a large pattern (a paragraph). Your report should contain some description of the algorithms and, most importantly, your findings. Include a graph showing the relation of RT against the text length. (This implies that you have to use several different lengths, which are placed on the x-axis of a graph.) The results should be reproducible.

  B) "Wacky Races"

  Prove empirically that there can be situations in which - Binary Sunday (the first algorithms covered in class) is at least twice as fast as Gusfield Z. - KMP is at least twice as fast as Rabin-Karp. - Rabin-Karp is at least twice as fast as Sunday It means that you should present a specific P and a specific T for which this happens. T should be at least 100kB long. The results should be reproducible.

** Part Two

"What was that char again?"

Implement the Brute-force and Sunday algorithms so that they accept wildcards ? and *.
Your implementation should produce a Boolean value of a match found or not.
The wildcards and \ itself can be escaped with a backslash.
Explain your extensions to the algorithms in your report.

*** Part three

"Jewish-style carp"

Devise a version of Rabin-Karp algorithm which will check if for a given
picture* M by N large its top-right K by K corner is duplicated somewhere in the picture.
Your algorithm should replace slow modulo prime operations with faster bitwise mask &'s.
!!!! Do make sure that the RT is at most linear in the number of pixels in the text !!!

* Here, picture is a two-dimensional array of arbitrary items.