Abstract
Given a sequence A of numbers and two positive integers ℓ and k, we study the problem to find k disjoint segments of A, each has length at least ℓ, such that their sum of densities is maximized. We give the first known polynomial-time algorithm for the problem: For general k, our algorithm runs in O(n ℓk) time. For the special case with k = 2 (respectively, k = 3), we also show how to solve the problem in O(n) (respectively, O(n + ℓ2)) time.
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Chen, Y.H., Lu, HI., Tang, C.Y. (2005). Disjoint Segments with Maximum Density. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428848_108
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DOI: https://doi.org/10.1007/11428848_108
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26043-1
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