准随机负载均衡
Quasirandom Load Balancing
摘要：
我们提出了一个简单的分布式算法平衡不可分割的令牌图。该算法是完全确定性的，尽管它试图通过保持累积的舍入误差尽可能小来模仿（和增强）随机算法。令人惊讶的是，我们的新算法非常接近重要网络拓扑上的理想化过程（令牌可分）。在具有n个节点的d维环面图上，它仅通过一个附加常数偏离理想化过程。与此相反，Friedrich和Sauerwald（2009）的随机舍入方法可以偏离到Omega（polylog（n）），Rabani，Sinclair和Wanka（1998）的确定性算法具有Omega（n^{1/d}）的偏差。这使得我们的quasirandom算法的第一个已知的算法，这是最佳的时间和实现平滑。我们进一步表明，也超立方体我们的算法有一个更小的偏离理想化的过程比以前的算法。
英文摘要：
We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm surprisingly closely approximates the idealized process (where the tokens are divisible) on important network topologies. On d-dimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant. In contrast to that, the randomized rounding approach of Friedrich and Sauerwald (2009) can deviate up to Omega(polylog(n)) and the deterministic algorithm of Rabani, Sinclair and Wanka (1998) has a deviation of Omega(n^{1/d}). This makes our quasirandom algorithm the first known algorithm for this setting which is optimal both in time and achieved smoothness. We further show that also on the hypercube our algorithm has a smaller deviation from the idealized process than the previous algorithms.
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