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Title:
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A TEXTILE DESIGN AND THE BOOLEAN RANK PROBLEM |
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Author(s):
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Isamu Matsuura , Mutsunori Yagiura , Tomio Hirata |
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ISBN:
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978-972-8924-97-3 |
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Editors:
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Hans Weghorn and Pedro Isaías |
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Year:
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2009 |
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Edition:
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V I, 2 |
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Keywords:
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Boolean rank, dobby loom, biclique cover, biclique partition |
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Type:
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Full Paper |
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First Page:
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345 |
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Last Page:
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352 |
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Language:
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English |
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Cover:
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Full Contents:
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click to dowload 
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Paper Abstract:
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A dobby loom is a weaving machine prevailing in the textile industry. The more heald frames a dobby loom is equipped
with, the more complicated designs of cloth can be woven. By introducing long-eye healds into a dobby loom, we can
reduce the number of heald frames required for a given design of cloth. It was shown that the number of necessary heald
frames equals the Boolean rank of a Boolean matrix associated with the design of cloth, and thus that the problem of
finding, for a given design of cloth, the minimum number of heald frames is NP-hard. Heuristic and exhaustive
algorithms have been proposed so far. In this paper, we consider a more realistic version of the problem and show that the
number of necessary heald frames equals the exclusive Boolean rank of the matrix. Based on this observation, we
propose a heuristic algorithm. |
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