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Re^3: Challenge: Fast Common Substrings (O(n)?)

by tye (Sage)
on Apr 04, 2007 at 21:53 UTC ( #608378=note: print w/ replies, xml ) Need Help??

in reply to Re^2: Challenge: Fast Common Substrings
in thread Challenge: Fast Common Substrings

The page you link to mentions being able to build them in O(n) but then only really describes how to go from a suffix tree for string $x to one for string $x.$c (1==length$c) in O(length $x). Using that algorithm would require O(N*N) to build the suffix tree for a string of length N.

So I'm not sure I believe the O(N) claim for building the whole suffix tree based on that page.

- tye        

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Re^4: Challenge: Fast Common Substrings (O(n)?)
by lima1 (Curate) on Apr 04, 2007 at 22:12 UTC
    The naive algorithm requires O(N*N). The Ukkonen algorithm needs only O(N). If you want to understand it - it is not trivial - I recommend Gusfields book (Algorithms on Strings,...).

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