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Linear compound algorithms for the partitioning problem

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  • Yong He
  • Hans Kellerer
  • Vladimir Kotov

Abstract

For a given set S of nonnegative integers the partitioning problem asks for a partition of S into two disjoint subsets S1 and S2 such that the sum of elements in S1 is equal to the sum of elements in S2. If additionally two elements (the kernels) r1, r2 ∈ S are given which must not be assigned to the same set Si, we get the partitioning problem with kernels. For these NP‐complete problems the authors present two compound algorithms which consist both of three linear greedylike algorithms running independently. It is shown that the worst‐case performance of the heuristic for the ordinary partitioning problem is 12/11, while the second procedure for partitioning with kernels has a bound of 8/7. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 593–601, 2000

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  • Yong He & Hans Kellerer & Vladimir Kotov, 2000. "Linear compound algorithms for the partitioning problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 593-601, October.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:7:p:593-601
    DOI: 10.1002/1520-6750(200010)47:73.0.CO;2-H
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    Cited by:

    1. Olawale James, GBADEYAN, & Jamiu Ola, IDRIS & Kayode Olawale, KUMOYE, & Tayo Akindele, ZUBAIR,, 2016. "Assessing The Security Of Learning Spaces In Selected Primary Schools Within Ilorin Metropolis," Ilorin Journal of Business and Social Sciences, Faculty of Social Sciences, University of Ilorin, vol. 18(2), pages 179-198, October.
    2. Federico Della Croce & Rosario Scatamacchia & Vincent T’kindt, 2019. "A tight linear time $$\frac{13}{12}$$ 13 12 -approximation algorithm for the $$P2 || C_{\max }$$ P 2 | | C max problem," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 608-617, August.
    3. Federico Della Croce & Rosario Scatamacchia, 2020. "The Longest Processing Time rule for identical parallel machines revisited," Journal of Scheduling, Springer, vol. 23(2), pages 163-176, April.

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