Finding the minimum number of elements with sum above a threshold

Authors:
Yan Jiang;Chaoyi Pang;Hao Lan Zhang;Junhu Wang;Tongliang Li;Qing Zhang;Jing He
Affiliations:
Center for Data Management & Intelligent Computing, NIT, Zhejiang University, Ningbo, China;Center for Data Management & Intelligent Computing, NIT, Zhejiang University, Ningbo, China and Applied Mathematics Institute, Hebei Academy of Sciences, Shijiazhuang, China and ICT Centre, CSIRO, ...;Center for Data Management & Intelligent Computing, NIT, Zhejiang University, Ningbo, China;Applied Mathematics Institute, Hebei Academy of Sciences, Shijiazhuang, China and School of Information and Communication Technology, Griffith University, Australia;Applied Mathematics Institute, Hebei Academy of Sciences, Shijiazhuang, China;ICT Centre, CSIRO, Brisbane, Australia;Centre for Applied Informatics, Victoria University, Australia
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

Motivated by the wavelet compression techniques and their applications, we consider the following problem: Given an unsorted array of numerical values and a threshold, what is the minimum number of elements chosen from the array, such that the sum of these elements is not less than the threshold value. In this article, we first provide two linear time algorithms for the problem. We then demonstrate the efficacy of these algorithms through experiments. Lastly, as an application of this research, we indicate that the construction of wavelet synopses on a prescribed error bound (in L"2 metric) can be solved in linear time.