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The least weight subsequence (LWS) problem is introduced, and is shown to be equivalent to the classic minimum path problem for directed graphs. A special case of the LWS problem is shown to be solvable in O(nlog n) time generally and, for certain weight functions, in linear time. A number of applications are given, including an optimum paragraph formation problem and the problem of finding a minimum height B-tree, whose solutions realize improvement in asymptotic time complexity.
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Hirschberg et al. (1987) studied this question.
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