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An improved lower bound for approximating the Minimum Integral Solution Problem with Preprocessing over $$\ell _\infty $$ ℓ ∞ norm

Author

Listed:
  • Wenbin Chen

    (Guangzhou University
    Fudan University
    Nanjing University)

  • Lingxi Peng

    (Guangzhou University)

  • Jianxiong Wang

    (Guangzhou University)

  • Fufang Li

    (Guangzhou University)

  • Maobin Tang

    (Guangzhou University)

  • Wei Xiong

    (Guangzhou University)

  • Songtao Wang

    (South China Normal University)

Abstract

In this paper, we study the approximation complexity of the Minimum Integral Solution Problem with Preprocessing introduced by Alekhnovich et al. (FOCS, pp. 216–225, 2005). We show that the Minimum Integral Solution Problem with Preprocessing over $$\ell _\infty $$ ℓ ∞ norm ( $$\hbox {MISPP}_\infty $$ MISPP ∞ ) is NP-hard to approximate to within a factor of $$(\log n)^{1/2-\epsilon },$$ ( log n ) 1 / 2 - ϵ , unless $$\mathbf{NP}\subseteq \mathbf{DTIME}(2^{poly log(n)}).$$ NP ⊆ DTIME ( 2 p o l y l o g ( n ) ) . This improves on the best previous result. The best result so far gave $$\sqrt{2}-\epsilon $$ 2 - ϵ factor hardness for any $$\epsilon >0.$$ ϵ > 0 .

Suggested Citation

  • Wenbin Chen & Lingxi Peng & Jianxiong Wang & Fufang Li & Maobin Tang & Wei Xiong & Songtao Wang, 2015. "An improved lower bound for approximating the Minimum Integral Solution Problem with Preprocessing over $$\ell _\infty $$ ℓ ∞ norm," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 447-455, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9646-4
    DOI: 10.1007/s10878-013-9646-4
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