## Abstract

Consider the multidimensional array matching problem, where differences between characters of the pattern and characters of the text are permitted. A difference may be due to a mismatch between a text and pattern character, superfluous text character or superfluous pattern character. Given a d-dimensional array of size n^{d} (text) and a d-dimensional array of size m^{d} pattern we present the following algorithms:. For a given k, find all occurrences of the pattern in the text with at most k differences. Our serial algorithm runs in time O(n^{d}(dk+k^{2})) and the parallel algorithm runs in time O(d(^{d}log n+ k)+k^{2}) using n^{d} processors. If superfluous characters are not allowed and the only permitted errors are mismatches, we solve the problem serially in time O(n^{d}dk) and in parallel in time O(d(^{d}logn+k)) using n^{d} processors. We present an alternate algorithm for the mismatches problem which runs serially in time O(2^{d}n^{d}log^{2} m) and in parallel in time O(d log n) using n^{d} processors. This algorithm is more efficient for large k. We also give an efficient solution to the close-match problem. Here a mismatch weight function f:Σ×Σ→[0,1] is assigned. The weight function gives weight to the mismatches, some mismatches being worse than others. We present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time O(2^{d}n^{d} log^{2} m). Our parallel algorithm is again of time complexity O(d log n) using n^{d} processors.

Original language | English |
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Pages (from-to) | 97-115 |

Number of pages | 19 |

Journal | Theoretical Computer Science |

Volume | 81 |

Issue number | 1 |

DOIs | |

State | Published - 22 Apr 1991 |

Externally published | Yes |

### Bibliographical note

Funding Information:* Supported by NSF under grant CCR-8803641. ** Supported by the Applied Mathematical Sciences Subprogram or the O@ce of Energy Research, U.S. Department of Energy, under corltract number DZ-AC02-76ER03077 by NSF under grant number CCR-8908286, and b> the New York State Science and Technology Foundation, Center for Ad~~anced Technology in Telecommunications, Polytechnic University, Brooklyn. NY.