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Multi-dimensional pattern matching with dimensional wildcards

  • Raffaele Giancarlo
  • Roberto Grossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 937)

Abstract

We introduce a new multi-dimensional pattern matching problem, which is a natural generalization of the on-line search in string matching. We are given a text matrix A[1: n1, ..., 1:n d ] of size N= n1×n2×...×n d , which we may preprocess. Then, we are given, online, an r-dimensional pattern matrix B[1:m1,...,1:m r ] of size M= m1×m2×...×m r , with 1≤r≤d. We would like to know whether B*=B*[*, 1:m1,*, ...,1: mr, *] occurs in A, where * is a dimensional wildcard such that B* is any d-dimensional matrix having size 1 × ... × m1×...1×m r ×...1 and containing the same elements as B. Notice that there might be (d/r)≤2d occurrences of B* for each position of A. We give CRCW-PRAM algorithms for preprocessing A in O(d log N) time with N2/n max processors, where n max =max|n1,...,n d }. The on-line search for B* can be done in O(d log M) time and optimal O(dM) work.

Keywords

Pattern Match Decomposition Tree String Match Suffix Tree Canonical Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Raffaele Giancarlo
    • 1
  • Roberto Grossi
    • 2
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di PalermoPalermoItaly
  2. 2.Dipartimento di Sistemi e InformaticaUniversità di FirenzeFirenzeItaly

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