Abstract
String matching (SM) problem is to find the occurrences of a pattern within a text. A vanable length don't care (VLDC) is a special symbol, not belonging to a finite alphabet ∑ but in ∑*. Each VLDC in the pattern can match any substring in the text. Given a run-length coded text of length 2n over ∑ and a run-length coded pattern of length 2m over ∑*, this paper first presents an O(1) time parallel SM algorithm for run-length coded strings with VLDCs on a reconfigurable mesh (RM) using O(nm) processors. Consider the hardware limitation in VLSI implementation. In order to be suitable for VLSI modular implementation, a partitionable parallel algorithm on the RM with limited processors is further presented. For N < n and M < m, the SM for run-length coded strings with VLDCs can be solved in O(X^Y^) time on the RM using O(NM)(= O((nm)/((X^Y^))) processors, where X^ = [(n – 1)/(N – 1)] and Y^ = [(m – 1)/(M – 1)].
Highlights
A basic search operation on patterns is the string matching (SM)
THEOREM The SM problem for run-length coded strings with variable length don’t care (VLDC) can be solved in O(1) time on the rn x n Reconfigurable mesh (RM)
Step 8 Case X is odd With the connection linking the W and S (N) for odd Y, each processor PE(i, j) holding (P(1, m), P(2, m)), processor PE(M,j) (PE(1,j)) holding the data sent from pipe Y + and processor PE(i,N) holding the data sent from pipe X+ 1, where l
Summary
A basic search operation on patterns is the string matching (SM). In many applications, using a special encoding method for representing strings is important and advantageous for saving storage and manipulating them. On the rn x n RM, our O(1) time parallel SM algorithm for run-length coded strings with VLDCs is presented in the following nine steps. Establish a vertical bus system for each column This configuration can be built by connecting the N and S ports of each processor. Establish a horizontal bus system for each row This configuration can be built by connecting the W and E ports of each processor. THEOREM The SM problem for run-length coded strings with VLDCs can be solved in O(1) time on the rn x n RM
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