An Improved Randomized Approximation Algorithm for Maximum Triangle Packing

  • Zhi-Zhong Chen
  • Ruka Tanahashi
  • Lusheng Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)


This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm and claimed that it achieves an expected ratio of \(\frac{89}{169}(1 - \epsilon)\) for any constant ε> 0. However, their analysis was flawed. We present a new randomized polynomial-time approximation algorithm for the problem which achieves an expected ratio very close to their claimed expected ratio.


Approximation Algorithm Random Choice Discrete Apply Mathematic Path Component Cycle Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chlebík, M., Chlebíková, J.: Approximating Hardness for Small Occurrence Instances of NP-Hard Problems. In: Petreschi, R., Persiano, G., Silvestri, R. (eds.) CIAC 2003. LNCS, vol. 2653, pp. 152–164. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)zbMATHGoogle Scholar
  3. 3.
    Hassin, R., Rubinstein, S.: An Approximation Algorithm for Maximum Triangle Packing. Discrete Applied Mathematics 154, 971–979 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Hassin, R., Rubinstein, S.: Erratum to gAn approximation algorithm for maximum triangle packingh: [Discrete Applied Mathematics 154 (2006) 971-979]. Discrete Applied Mathematics 154, 2620–2620 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kann, V.: Maximum Bounded 3-Dimensional Matching Is MAX SNP-Complete. Information Processing Letters 37, 27–35 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Raghavan, P.: Probabilistic Construction of Deterministic Algorithms: Approximating Packing Integer Programs. Journal of Computer and System Sciences 38, 683–707 (1994)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Zhi-Zhong Chen
    • 1
  • Ruka Tanahashi
    • 1
  • Lusheng Wang
    • 2
  1. 1.Department of Mathematical SciencesTokyo Denki UniversityHatoyamaJapan
  2. 2.Department of Computer ScienceCity University of Hong KongHong Kong 

Personalised recommendations