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Ranking k maximum sums
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science.
2007 (English)In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 377, no 1-3, p. 229-237Article in journal (Refereed) Published
Abstract [en]

Given a sequence of n real numbers and an integer parameter k, the problem studied in this paper is to compute k subsequences of consecutive elements with the sums of their elements being the largest, the second largest, and the kth largest among all possible range sums of the input sequence. For any value of k, 1 <= k <= n (n + 1)/2, we design a fast algorithm that takes O (n + k log n) time in the worst case to compute and rank all such subsequences. We also prove that our algorithm is optimal for k = O (n) by providing a matching lower bound.Moreover, our algorithm is an improvement over the previous results on the maximum sum subsequences problem (where only the subsequences are requested and no ordering with respect to their relative sums will be determined).Furthermore, given the fact that we have computed the fth largest sums, our algorithm retrieves the (l + 1)th largest sum in O (log n) time, after O (n) time of preprocessing.

Place, publisher, year, edition, pages
2007. Vol. 377, no 1-3, p. 229-237
National Category
Computer Sciences
Research subject
Dependable Communication and Computation Systems
Identifiers
URN: urn:nbn:se:ltu:diva-2927DOI: 10.1016/j.tcs.2007.03.011ISI: 000247279200017Scopus ID: 2-s2.0-34247634994Local ID: 0a9d4820-5ac1-11dc-8a1d-000ea68e967bOAI: oai:DiVA.org:ltu-2927DiVA, id: diva2:975781
Note
Validerad; 2007; 20070904 (pafi)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Bengtsson, FredrikChen, Jingsen

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