网络速度缩放中的竞争比与网络无关
Network Speed Scaling with Competitive Ratios Independent of the Network
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中文总结 AI 辅助
针对网络速度缩放问题，提出一种通过凸规划路由并以固定速度运行服务器的算法，其竞争比仅依赖功率函数，对$P(s)=s^2$至多为黄金比例，并证明现有路由规则可能远非最优。
中文摘要 AI 辅助
在网络速度缩放问题中，作业随时间到达一个服务器网络，这些服务器的速度可以调节，每个作业必须由服务器沿其允许的路线之一处理，目标是最小化总流时间加上总能量。对于随机到达，Vaze和Nair的竞争比依赖于网络，具体通过其使用的路线长度。我们表明这种依赖可以被消除：我们给出一种算法，该算法通过求解凸规划来路由作业，并以固定速度运行每台服务器，其竞争比仅取决于功率函数；对于$P(s)=s^2$，它至多为黄金比例$\varphi\approx1.618$。关键思想是对最优成本的下界，该下界与我们的算法成本一样，是每台服务器负载函数的和，因此分析简化为单服务器。我们还表明，Vaze和Nair的路由规则可能比最优差$\Omega(L)$倍，其中$L$是最长路线的长度。
英文摘要
In network speed scaling, jobs arrive over time at a network of servers whose speeds can be tuned, every job must be processed by the servers along one of its allowed routes, and the goal is to minimize the total flow time plus the total energy. For stochastic arrivals, the competitive ratio of Vaze and Nair depends on the network, through the lengths of the routes it uses. We show that this dependence can be removed: we give an algorithm, which routes the jobs by solving a convex program and runs every server at a fixed speed, whose competitive ratio depends only on the power functions; for $P(s)=s^2$, it is at most the golden ratio $φ\approx1.618$. The key idea is a lower bound on the optimal cost which, like the cost of our algorithm, is a sum over the servers of a function of each server's load, so the analysis reduces to a single server. We also show that the routing rule of Vaze and Nair can be a factor $Ω(L)$ away from optimal, where $L$ is the length of the longest route.
