More Pep for Boyer-Moore Grep (part 2 of 2)

[James A. Woods]

#  "Gratiano speaks an infinite deal of nothing, more than any man in all
   of Venice.  His reasons are as two grains of wheat hid in two bushels of
   chaff:  you shall seek all day ere you find them, they are not worth
   the search."  -- Shakespeare, Merchant of Venice

... or, part 2, "Reach out and Boyer-Moore Egrep Someone"

     Maybe you never use 'grep'.  Then ignore this.  But if you do, why not
use the best algorithm?  Serious addicts know that for unstructured yet
stable text, B-trees are used for speed, or something like Lesk's nifty
(and unavailable) 'grab' suite for inverted files are ways to go.  Barring file
inversion daemons for netnews and other ephemera, we are limited to the
present improvements.

     Proper skeptics should question why a nearly I/O-bound program
(but not for any CPU with less than the power of a 780, alas) should be
made more so.  The question was posed in B & M's classic 1978 CACM
paper -- the answer then was to free up more CPU cycles for timesharing.
Now, our motivations are more mundane (we won't have desktop 5 MIP machines
for another year), but not only that, we've discovered that the Cray 2's
standard 'egrep' is also very anemic, performing 8-12 times as worse as ours
on simple patterns.  For shame, especially since hearing of the rumor that
certain group theorists have a search application ready for testing.
Boyer-Moore could fill in until a Cray vectorizing C compiler shows up.
Sheer speed for machines whose filesystems are cached in memory is nice too.

     A quick-and-dirty rundown of the debts to which the new hybrid pays
now follows.

	Thompson, K. T. (CACM, November 1968):
		Regular Expression Search Algorithm.  As usual, obvious
		once you understand it.  The current 'egrep'.  Still
		useful as a base.  Abstracted by Aho/Ullman as Algorithm
		9.1 in Design and Analysis of Computer Algorithms.

	Boyer/Moore:
		Not quite pre-Unix.  Oh well.  Modern designers should
		know better now, if they want their stuff to get out there.
		By the way, I haven't used delta2 (or 1) since the O(mn) case
		case doesn't come up too often.  Sure Knuth stood on his head
		to better the linearity, but his proof had a bug in it until
		the 1980 SIAM J. Comput. retraction.  Would you want to code
		something that even Knuth trips up on?

 		Now to assuage nagging feelings that geneticists might want
		to search entire libraries of 9000-unit nucleotide protein
		sequences for ((AGCA|TTGCA).*TGC)|AGCT)?T?A+ or some nonsense
		which MIGHT be nonlinear, you would want delta2.  So convince
		someone to do the Galil/Apostolico/Giancarlo 2n comparison
		worst case stuff.  See egrep.c for reference.
		
	Gosper, W. (HAKMEM 1972):
		Gosper didn't get around to the Thompson-like machine until
		1972 with HAKMEM.  His PDP 10 code is nevertheless valiant.
		He is also (barely) credited with conceiving the backwards
		match idea independently.  Where is he now?
		
	Morris/Pratt:
		Nice guys, but for this purpose, has-beens.
		Neat to see a hacker's triumph bury some theory.

	Horspool (Software Practice & Experience, 1980):
		Now here's a Canadian after the heart of things
		(perfect hashing, text compression, NP-complete
		code generation probs., etc.)  Did some Amdahl
		timings to show that delta2 is not so hot.
		Knows about Search For Least Frequent Character First,
		which is useful for short patterns. 

	{,e,f}grep man page:
		The laughable bugnote "but we do not know a single algorithm
		that spans a wide enough range of space-time tradeoffs"
		certainly presumes that there is no such thing as switching
		logic.  How the 'grep' family got into a multiple-version
		mess is probably a Guy Harris story; 'egrep' looks like the
		winner, as its functionality is pretty much a superset of
		the other two.  The K & P teaser (p. 105) offers hope for
		unification, but we see no difference with extant V8 code.

     "Not cited in the text" -- the sexy randomized Karp/Rabin string searcher
(Sedgewick, Algorithms, or Karp's Turing Award Lecture), and the ribald classic
Time Warps, String Edits, and Macromolecules -- The Theory and Practice
of Sequence Comparison (Kruskal & Sankoff).  Inquire within.
Thanks for your patience,

     James A. Woods (ames!jaw)
     NASA Ames Research Center

P.S.
     Current applications for Boyer-Moore code include modification of 
'fastfind' for true speed, as well as substring search for 'grab', both
benefiting from BM-style search thru incrementally-compressed files/indices.