期刊
SIAM JOURNAL ON COMPUTING
卷 41, 期 3, 页码 565-586出版社
SIAM PUBLICATIONS
DOI: 10.1137/110844210
关键词
scheduling; min-sum objective; single machine; unreliable machine; machine speed; universal solution; worst case guarantee
资金
- EU [215270 FRONTS]
- DFG research center MATHEON in Berlin
- Tinbergen Institute
We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. Our objective is to minimize Sigma w(j)f(C-j) for any nondecreasing, nonnegative, differentiable cost function f(C-j). We aim for a universal solution that performs well without adaptation for all cost functions for any possible machine behavior. We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both performance guarantees are best possible for any unbounded cost function. Our algorithms can be adapted to run in polynomial time with slightly increased cost. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Omega(log n/log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据