Given a list of strings, build a DAG in which each node is a string and there is an edge x->y iff x is proper substring of y?

Revision en2, by pabloskimg, 2018-10-21 07:45:53

There are at most N = 10^4 strings, but the length of the concatenation of all strings is at most MAXLEN = 10^6. What would be the more efficient way to build a DAG as described in the title? The naive way would be comparing each pair of strings (X,Y), which leads to O(N^2) comparisons, and then for each pair to check whether X is substring of Y in O(MAXLEN^2). The naive solution could be improved by first sorting strings by length so that each string X can only be substring of strings to the right, and also we could use Rolling Hashing to reduce the complexity of substring verification to O(MAXLEN). Is it possible to do even better? I've got the feeling that Suffix Array could be of help, but I'm not sure of exactly how. The motivating problem is this one

Tags #strings, substring search

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en5 English pabloskimg 2018-10-21 17:55:36 1
en4 English pabloskimg 2018-10-21 07:50:28 63
en3 English pabloskimg 2018-10-21 07:47:51 12 Tiny change: 'substring verification to O(MAXL' -> 'substring search to O(MAXL'
en2 English pabloskimg 2018-10-21 07:45:53 7
en1 English pabloskimg 2018-10-21 07:45:01 1009 Initial revision (published)