Combinatorial Pattern Matching: 12th Annual Symposium, CPM by Gad M. Landau (auth.), Amihood Amir (eds.) PDF

By Gad M. Landau (auth.), Amihood Amir (eds.)

ISBN-10: 3540422714

ISBN-13: 9783540422716

ISBN-10: 354048194X

ISBN-13: 9783540481942

This publication constitutes the refereed complaints of the twelfth Annual Symposium on Combinatorial development Matching, CPM 2001, held in Jerusalem, Israel, in July 2001.
The 21 revised papers provided including one invited paper have been rigorously reviewed and chosen from 35 submissions. The papers are dedicated to present theoretical and algorithmic problems with looking and matching strings and extra complex styles resembling timber, commonplace expressions, graphs, element units, and arrays in addition to to complex functions of CPM in parts akin to the web, computational biology, multimedia structures, info retrieval, info compression, coding, laptop imaginative and prescient, and trend popularity.

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Extra resources for Combinatorial Pattern Matching: 12th Annual Symposium, CPM 2001 Jerusalem, Israel, July 1–4, 2001 Proceedings

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The decoding routine can thus address earlier locations as if the blocks, that are ancestors of the current block in the tree layout, were stored contiguously. Any element of the form (off, len) in block Bi can point back into a block Bj , with j = i/2b for b = 0, 1, . . , log2 i , and the index of this block can be calculated by b ←− (off − cur + 1)/Blocksize , where cur is the index of the current position in block Bi . The formal decoding procedure is given in Figure 5. Parallel Lempel Ziv Coding PLZSS-decode(i, j) { cur ←− 1 while there are more items to decode { if next item is a character { store the character else { } } } perform in parallel Figure 5: cur ←− cur + 1 25 } // the item is (off, len) if off < cur // pointer within block Bi copy len characters, starting at position cur−off else // pointer to earlier block { b ←− (off − cur + 1)/Blocksize t ←− (off − cur) mod Blocksize copy len characters, starting at position t in block B i/2b which is stored in Pf ( } i/2b ) cur ←− cur + len if 2i ≤ n if 2i + 1 ≤ n PLZSS-decode (2i, j) PLZSS-decode (2i + 1, i + 1) Parallel LZSS decoding for block Bi on processor Pj .

Note that the size of the history window is usually limited by some constant W . We do not impose any such limit, but in fact, the encoding of any element is based on a history of size at most log2 n × the block size. For the decoding, recall that we assume that the encoded blocks are of equal size Blocksize. The decoding routine can thus address earlier locations as if the blocks, that are ancestors of the current block in the tree layout, were stored contiguously. Any element of the form (off, len) in block Bi can point back into a block Bj , with j = i/2b for b = 0, 1, .

Define r(i) as the largest power of 2 that divides the integer i, that is, r(i) is the length of the longest suffix consisting only of zeros of the binary representation of i. i 1 Claim: f(i) = +1 . 2 2r(i) Proof: By induction on i. For i = 1, we get f(1) = 1, which is correct. Assume the claim is true up to i − 1. If i is odd, r(i) = 0 and the formula gives f(i) = (i + 1)/2. As has been mentioned above, any oddly indexed block is the starting point of a new processor and indeed processor P(i+1)/2 starts at block Bi .

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Combinatorial Pattern Matching: 12th Annual Symposium, CPM 2001 Jerusalem, Israel, July 1–4, 2001 Proceedings by Gad M. Landau (auth.), Amihood Amir (eds.)


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