Skip to main content
Springer Nature Link
Log in

Online Semi-matching Problem with Two Heterogeneous Sensors in a Metric Space

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13595))

Included in the following conference series:

Abstract

In this paper, we consider the online semi-matching problem with two heterogeneous sensors \(s_1\) and \(s_2\) in a metric space (X, d), where \(d(\cdot , \cdot )\) is a distance function. If a request r is assigned to sensor \(s_1\), then the matching cost is \(d(r,s_1)\); otherwise, the matching cost is \(\frac{d(r,s_2)}{w}\), where \(w\ge 1\) is the weight of sensor \(s_2\). The goal is to minimize the total cost of matching all requests. We design an optimal online algorithm with a competitive ratio of \(1+w+\frac{\sqrt{w}}{w}\) for \(1<w\le \alpha \), and an optimal online algorithm with a competitive ratio of w for \(w>\alpha \), where \(\alpha \approx 3.382\).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Anthony, B.M., Chung, C.: Online bottleneck matching. J. Combin. Optim. 27(1), 100–114 (2014). https://doi.org/10.1007/s10878-012-9581-9

    Article  MathSciNet  MATH  Google Scholar 

  2. Antoniadis, A., Barcelo, N., Nugent, M., Pruhs, K., Scquizzato, M.: A \(o(n)\)- competitive deterministic algorithm for online matching on a line. Algorithmica 81, 2917–2933 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bansal, N., Buchbinder, N., Gupta, A., Naor, J.S.: A randomized \(O(\log ^2k)\)-competitive algorithm for metric bipartite matching. Algorithmica 68, 390–403 (2014). https://doi.org/10.1007/s00453-012-9676-9

    Article  MathSciNet  MATH  Google Scholar 

  4. Fuchs, B., Hochstattler, W., Kern, W.: Online matching on a line. Theor. Comput. Sci. 332(1), 251–264 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gupta, A., Lewi, K.: The online metric matching problem for doubling metrics. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) Automata, Languages, and Programming, ICALP 2012. LNCS, vol. 7391, pp. 424–435. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31594-7_36

  6. Idury, R., Schaffer, A.A.: A better lower bound for on-line bottleneck matching (1992)

    Google Scholar 

  7. Itoh, T., Miyazaki, S., Satake, M.: Competitive analysis for two variants of online metric matching problem. Discret. Math. Algorithms Appl. 13, 2150156 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kalyanasundaram, B., Pruhs, K.: Online weighted matching. J. Algorithms 14(3), 478–488 (1993). Preliminary version appeared in Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete algorithms (SODA), pp. 234–240 (1991)

    Google Scholar 

  9. Khuller, S., Mitchell, S.G., Vazirani, V.V.: On-line algorithms for weighted bipartite matching and stable marriages. Theoret. Comput. Sci. 127(2), 255–267 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, W., Li, J., Guan, L., Shi, Y.: The prize-collecting call control problem on weighted lines and rings. RAIRO-Oper. Res. 50(1), 39–46 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Meyerson, A., Nanavati, A., Poplawski, L.: Randomized online algorithms for minimum metric bipartite matching. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm(SODA), pp 954–959 (2006)

    Google Scholar 

  12. Nayyar, K., Raghvendra, S.: An input sensitive online algorithm for the metric bipartite matching problem. In: Proceedings of IEEE 58th Annual Symposium on Foundations of Computer Science, pp. 505–515. (2017)

    Google Scholar 

  13. Peserico, E., Scquizzato, M.: Matching on the line admits no \(o(\sqrt{\log n})\)-competitive algorithm. In: Proceedings of the 48th International Colloquium on Automata, Languages, and Programming (ICALP), Article 103 (2021)

    Google Scholar 

  14. Raghvendra, S.: A robust and optimal online algorithm for minimum metric bipartite matching. In: Proceedings of Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016), ID 18 (2016)

    Google Scholar 

  15. Raghvendra, S.: Optimal analysis of an online algorithm for the bipartite matching problem on a line. In: Proceedings of 34th International Symposium on Computational Geometry, ID 67 (2017)

    Google Scholar 

  16. Xiao, M., Zhao, S., Li, W., Yang, J.: Online bottleneck semi-matching. In: Du, D.-Z., Du, D., Wu, C., Xu, D. (eds.) Combinatorial Optimization and Applications, COCOA 2021. LNCS, vol. 13135, pp. 445–455. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92681-6_35

Download references

Acknowledgement

The work is supported in part by the National Natural Science Foundation of China [No. 12071417].

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Yunnan University, Kunming, 650504, People’s Republic of China

    Man Xiao & Weidong Li

Authors
  1. Man Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weidong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weidong Li .

Editor information

Editors and Affiliations

  1. Shenzhen Institute of Advanced Technology, Shenzhen, China

    Yong Zhang

  2. Harbin Institute of Technology, Harbin, China

    Dongjing Miao

  3. Technical University of Berlin, Berlin, Germany

    Rolf Möhring

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Xiao, M., Li, W. (2022). Online Semi-matching Problem with Two Heterogeneous Sensors in a Metric Space. In: Zhang, Y., Miao, D., Möhring, R. (eds) Computing and Combinatorics. COCOON 2022. Lecture Notes in Computer Science, vol 13595. Springer, Cham. https://doi.org/10.1007/978-3-031-22105-7_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-22105-7_39

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22104-0

  • Online ISBN: 978-3-031-22105-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation