IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v43y2022i1d10.1007_s10878-021-00754-w.html
   My bibliography  Save this article

Some graph optimization problems with weights satisfying linear constraints

Author

Listed:
  • Kameng Nip

    (Xiamen University)

  • Tianning Shi

    (Tsinghua University)

  • Zhenbo Wang

    (Tsinghua University)

Abstract

In this paper, we study several graph optimization problems in which the weights of vertices or edges are variables determined by several linear constraints, including maximum matching problem under linear constraints (max-MLC), minimum perfect matching problem under linear constraints (min-PMLC), shortest path problem under linear constraints (SPLC) and vertex cover problem under linear constraints (VCLC). The objective of these problems is to decide the weights that are feasible to the linear constraints, and find the optimal solutions of corresponding graph optimization problems among all feasible choices of weights. We find that these problems are NP-hard and are hard to be approximated in general. These findings suggest us to explore various special cases of them. In particular, we show that when the number of constraints is a fixed constant, all these problems are polynomially solvable. Moreover, if the total number of distinct weights is a fixed constant, then max-MLC, min-PMLC and SPLC are polynomially solvable, and VCLC has a 2-approximation algorithm. In addition, we propose approximation algorithms for various cases of max-MLC.

Suggested Citation

  • Kameng Nip & Tianning Shi & Zhenbo Wang, 2022. "Some graph optimization problems with weights satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 200-225, January.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:1:d:10.1007_s10878-021-00754-w
    DOI: 10.1007/s10878-021-00754-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-021-00754-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-021-00754-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhenbo Wang & Kameng Nip, 2017. "Bin packing under linear constraints," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1198-1209, November.
    2. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    3. Nip, Kameng & Wang, Zhenbo & Wang, Zizhuo, 2016. "Scheduling under linear constraints," European Journal of Operational Research, Elsevier, vol. 253(2), pages 290-297.
    4. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    5. Kameng Nip & Zhenbo Wang & Zizhuo Wang, 2017. "Knapsack with variable weights satisfying linear constraints," Journal of Global Optimization, Springer, vol. 69(3), pages 713-725, November.
    6. Siyun Zhang & Kameng Nip & Zhenbo Wang, 0. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhengxi Yang & Zhipeng Jiang & Wenguo Yang & Suixiang Gao, 2023. "Balanced graph partitioning based on mixed 0-1 linear programming and iteration vertex relocation algorithm," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-17, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Siyun Zhang & Kameng Nip & Zhenbo Wang, 2022. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1724-1740, October.
    2. Siyun Zhang & Kameng Nip & Zhenbo Wang, 0. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    3. András Frank, 2005. "On Kuhn's Hungarian Method—A tribute from Hungary," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 2-5, February.
    4. Amit Kumar & Anila Gupta, 2013. "Mehar’s methods for fuzzy assignment problems with restrictions," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 27-44, March.
    5. Parvin Ahmadi & Iman Gholampour & Mahmoud Tabandeh, 2018. "Cluster-based sparse topical coding for topic mining and document clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 537-558, September.
    6. Chenchen Ma & Jing Ouyang & Gongjun Xu, 2023. "Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 175-207, March.
    7. Tran Hoang Hai, 2020. "Estimation of volatility causality in structural autoregressions with heteroskedasticity using independent component analysis," Statistical Papers, Springer, vol. 61(1), pages 1-16, February.
    8. Chen, Lin & Ye, Deshi & Zhang, Guochuan, 2018. "Parallel machine scheduling with speed-up resources," European Journal of Operational Research, Elsevier, vol. 268(1), pages 101-112.
    9. Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.
    10. Caplin, Andrew & Leahy, John, 2020. "Comparative statics in markets for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 80-94.
    11. Biró, Péter & Gudmundsson, Jens, 2021. "Complexity of finding Pareto-efficient allocations of highest welfare," European Journal of Operational Research, Elsevier, vol. 291(2), pages 614-628.
    12. Péter Biró & Flip Klijn & Xenia Klimentova & Ana Viana, 2021. "Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange," Working Papers 1235, Barcelona School of Economics.
    13. Michal Brylinski, 2014. "eMatchSite: Sequence Order-Independent Structure Alignments of Ligand Binding Pockets in Protein Models," PLOS Computational Biology, Public Library of Science, vol. 10(9), pages 1-15, September.
    14. Chiwei Yan & Helin Zhu & Nikita Korolko & Dawn Woodard, 2020. "Dynamic pricing and matching in ride‐hailing platforms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(8), pages 705-724, December.
    15. Fanrong Xie & Anuj Sharma & Zuoan Li, 2022. "An alternate approach to solve two-level priority based assignment problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 613-656, March.
    16. Yan, Pengyu & Lee, Chung-Yee & Chu, Chengbin & Chen, Cynthia & Luo, Zhiqin, 2021. "Matching and pricing in ride-sharing: Optimality, stability, and financial sustainability," Omega, Elsevier, vol. 102(C).
    17. Guo, Yuhan & Zhang, Yu & Boulaksil, Youssef, 2021. "Real-time ride-sharing framework with dynamic timeframe and anticipation-based migration," European Journal of Operational Research, Elsevier, vol. 288(3), pages 810-828.
    18. Parhizkar, Tarannom & Mosleh, Ali & Roshandel, Ramin, 2017. "Aging based optimal scheduling framework for power plants using equivalent operating hour approach," Applied Energy, Elsevier, vol. 205(C), pages 1345-1363.
    19. Demetrescu, Camil & Lupia, Francesco & Mendicelli, Angelo & Ribichini, Andrea & Scarcello, Francesco & Schaerf, Marco, 2019. "On the Shapley value and its application to the Italian VQR research assessment exercise," Journal of Informetrics, Elsevier, vol. 13(1), pages 87-104.
    20. Christian Billing & Florian Jaehn & Thomas Wensing, 2020. "Fair task allocation problem," Annals of Operations Research, Springer, vol. 284(1), pages 131-146, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:43:y:2022:i:1:d:10.1007_s10878-021-00754-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.