# American Institute of Mathematical Sciences

October  2008, 4(4): 817-826. doi: 10.3934/jimo.2008.4.817

## Bounds on delay start LPT algorithm for scheduling on two identical machines in the $l_p$ norm

 1 Department of Fundamental Education, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China 2 Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, China, China

Received  May 2008 Revised  August 2008 Published  November 2008

In this paper, we consider the scheduling problem on two identical machines with objective to minimize the sum of the $l_{p}$ norm of every machine's load. We present the worst-case ratio of $DSL(l)$ for any integer $l$, here $DSL(l)$ first assigns the $l-1$ largest jobs optimally, then assigns the remaining jobs by $LS$ rule. It follows that $DSL(l)$ is an all-norm $\frac{l+2}{l+1}$ -approximation algorithm. Improved tight bound is given for $l=7$ in the $l_{2}$ norm.
Citation: Ling Lin, Dong He, Zhiyi Tan. Bounds on delay start LPT algorithm for scheduling on two identical machines in the $l_p$ norm. Journal of Industrial & Management Optimization, 2008, 4 (4) : 817-826. doi: 10.3934/jimo.2008.4.817
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