The structural border array

  • Authors:

  • Richard Beal;Donald A. Adjeroh

  • Affiliations:

  • -;-

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2013

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Abstract

The border and parameterized border (p-border) arrays are data structures used in pattern matching applications for traditional strings from the constant alphabet @S, and parameterized strings (p-strings) from the constant alphabet @S and the parameter alphabet @P. In this work, we introduce the structural border array (s-border) as defined for an n-length structural string (s-string) T. The s-string is a p-string with the existence of symbol complements in some alphabet @C. These different alphabets add to both the intricacies and capabilities of pattern matching. For example, the s-string can handle the Watson-Crick base pairings in biological sequences and thus, assists in applications that deal with efficient pattern matching between RNA strands that share similar secondary structures. Initially, we provide a construction that executes in O(n^2) time to build the s-border array. The paper establishes theory to improve the result to O(n) by proving particular properties of the s-border data structure. This result is significant because of the generalization of the s-string, which is a step beyond the p-string. Using the same construction algorithm, we show how to modify the s-string alphabets to also construct the p-border and the traditional border arrays in linear time. The generality of the s-border construction algorithm motivates us to devise pattern matching algorithms for s-matching, p-matching, and traditional matching. Our pattern matching algorithms are ultimately used to address the p-match problem with run-length encoded strings.