Improved Approximation Algorithm for the Combination of Parallel Machine Scheduling and Vertex Cover

This paper studies the combination problem of parallel machine scheduling and the vertex cover problem. Wang and Cui developed a (3 − 2 m+1)-approximation algorithm for this problem [13], where m is the number of parallel machines. We reduce the approximation factors from 2.33 to 2.25 for m = 2, from 2.5 to 2.33 for m = 3, and to 3 − 3 m+1 for m ≥ 4.

[1]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[2]  Zhenhua Cui,et al.  Combination of parallel machine scheduling and vertex cover , 2012, Theor. Comput. Sci..

[3]  S. Safra,et al.  On the hardness of approximating minimum vertex cover , 2005 .

[4]  Dror Rawitz,et al.  Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004 , 2004, CSUR.

[5]  Gerhard J. Woeginger,et al.  Vertex Cover Meets Scheduling , 2015, Algorithmica.

[6]  David P. Williamson.  The primal-dual method for approximation algorithms , 2002, Math. Program..

[7]  Subhash Khot,et al.  Vertex cover might be hard to approximate to within 2-/spl epsiv/ , 2003, 18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings..

[8]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.