Abstract
By restricting weight functions to satisfy the quadrangle inequality or the inverse quadrangle inequality, significant progress has been made in developing efficient sequential algorithms for the least-weight subsequence problem [10], [9], [12], [16]. However, not much is known on the improvement of the naive parallel algorithm for the problem, which is fast but demands too many processors (i.e., it takesO(log2 n) time on a CREW PRAM with n3/logn processors). In this paper we show that if the weight function satisfies the inverse quadrangle inequality, the problem can be solved on a CREW PRAM in O(log2 n log logn) time withn/log logn processors, or in O(log2 n) time withn logn processors. Notice that the processor-time complexity of our algorithm is much closer to the almost linear-time complexity of the best-known sequential algorithm [12].
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Communicated by Takao Nishizeki.
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Lam, T.W., Chan, Kf. Finding least-weight subsequences with fewer processors. Algorithmica 9, 615–628 (1993). https://doi.org/10.1007/BF01190159
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DOI: https://doi.org/10.1007/BF01190159