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Combinatorial approximation algorithms for the maximum bounded connected bipartition problem

Author

Listed:
  • Xiaofei Liu

    (Yunnan University)

  • Yajie Li

    (Yunnan University)

  • Weidong Li

    (Yunnan University
    Yunnan Center of Applied Mathematics)

  • Jinhua Yang

    (Dianchi College)

Abstract

In this paper, we study the maximum bounded connected bipartition problem: given a vertex-weighted connected graph $$G=(V,E;w)$$ G = ( V , E ; w ) and an upper bound B, the vertex set V is partitioned into two subsets $$(V_1,V_2)$$ ( V 1 , V 2 ) such that the total weight of the two subgraphs induced by $$V_1$$ V 1 and $$V_2$$ V 2 is maximized, and these subgraphs are connected, where the weight of a subgraph is the minimum of B and the total weight of all vertices in the subgraph. In this paper, we prove that this problem is NP-hard even when G is a completed graph, a grid graph with only 3 rows or an interval graph, and we present an $$\frac{8}{7}$$ 8 7 -approximation algorithm. In particular, we present a $$\frac{14}{13}$$ 14 13 -approximation algorithm for the case of grid graphs, and we present a fully polynomial-time approximation scheme for the case of interval graphs.

Suggested Citation

  • Xiaofei Liu & Yajie Li & Weidong Li & Jinhua Yang, 2023. "Combinatorial approximation algorithms for the maximum bounded connected bipartition problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00981-9
    DOI: 10.1007/s10878-022-00981-9
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    References listed on IDEAS

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    1. Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
    2. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
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    5. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.
    6. Byung-Cheon Choi & Myoung-Ju Park & Kyung Min Kim & Yunhong Min, 2021. "A Parallel Machine Scheduling Problem Maximizing Total Weighted Early Work," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(06), pages 1-16, December.
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