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 nd (text) and a d-dimensional array of size md 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(nd(dk+k2)) and the parallel algorithm runs in time O(d(dlog n+ k)+k2) using nd processors. If superfluous characters are not allowed and the only permitted errors are mismatches, we solve the problem serially in time O(nddk) and in parallel in time O(d(dlogn+k)) using nd processors. We present an alternate algorithm for the mismatches problem which runs serially in time O(2dndlog2 m) and in parallel in time O(d log n) using nd 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(2dnd log2 m). Our parallel algorithm is again of time complexity O(d log n) using nd processors.
Bibliographical noteFunding 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.