On locating disjoint segments with maximum sum of densities

Authors:
Hsiao-Fei Liu;Kun-Mao Chao
Affiliations:
Department of Computer Science and Information Engineering;Department of Computer Science and Information Engineering
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

Given a sequence A of n real numbers and two positive integers l and k, where $k \leq \frac{n}{l}$, the problem is to locate k disjoint segments of A, each has length at least l, such that their sum of densities is maximized. The best previously known algorithm, due to Bergkvist and Damaschke [1], runs in O(nl+k2l2) time. In this paper, we give an O(n+k2llogl)-time algorithm.