Border Array for Structural Strings

  • Richard Beal
  • Donald Adjeroh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)


The border and parameterized border (p-border) arrays are data structures used in pattern matching applications for traditional strings from the constant alphabet Σ and parameterized strings (p-strings) from the constant alphabet Σ and the parameter alphabet Π. In this work, we introduce the structural border (s-border) array 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 Γ. These different alphabets add to both the intricacies and capabilities of pattern matching. 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.


structural matching parameterized matching structural string parameterized string parameterized border s-match p-match s-string p-string p-border border 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Richard Beal
    • 1
  • Donald Adjeroh
    • 1
  1. 1.Lane Department of Computer Science and Electrical EngineeringWest Virginia UniversityMorgantownUSA

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