Pattern Matching for Permutations

نویسندگان

  • Prosenjit Bose
  • Jonathan F. Buss
  • Anna Lubiw
چکیده

Given a permutation T of 1 to n, and a permutation P of 1 to k, for k ≤ n, we wish to find a k-element subsequence of T whose elements are ordered according to the permutation P . For example, if P is (1, 2, . . . , k), then we wish to find an increasing subsequence of length k in T ; this special case can be done in time O(n log log n) [CW]. We prove that the general problem is NP-complete. We give a polynomial time algorithm for the decision problem, and the corresponding counting problem, in the case that P is separable—i.e. contains neither the subpattern (3, 1, 4, 2) nor its reverse, the subpattern (2, 4, 1, 3).

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تاریخ انتشار 1993