并行随机负载均衡的紧界
Tight Bounds for Parallel Randomized Load Balancing
摘要：
我们探讨了分布式balls-into-bins算法的基本限制。我们提出了一个自适应对称算法，实现了一个二进制负载在log* n+O（1）通信轮使用O（n）的消息。较大的仓负载可以换取较小的时间复杂度。我们证明了对称算法的时间复杂度的匹配下界为（1-o（1））log* n，该算法保证了小bin负载的渐近最优消息复杂度为O（n）。对于每一个假设的下限，我们提供了一个算法违反它，反过来实现恒定的最大仓负载在恒定的时间。作为应用，我们考虑以下问题。给定一个由n个节点组成的全连通图，其中每个节点需要发送和接收多达n条消息，并且在每一轮中，每个节点可以通过每条链路发送一条消息，将所有消息尽快传递到目的地。我们给出了一个简单的和强大的算法的时间复杂度O（log* n）为这项任务，并提供了一个概括的情况下，所有节点最初持有任意组的消息。一个不太实用的算法在渐近最优O（1）轮内终止。所有这些界限都以很高的概率成立。
英文摘要：
We explore the fundamental limits of distributed balls-into-bins algorithms. We present an adaptive symmetric algorithm that achieves a bin load of two in log* n+O(1) communication rounds using O(n) messages in total. Larger bin loads can be traded in for smaller time complexities. We prove a matching lower bound of (1-o(1))log* n on the time complexity of symmetric algorithms that guarantee small bin loads at an asymptotically optimal message complexity of O(n). For each assumption of the lower bound, we provide an algorithm violating it, in turn achieving a constant maximum bin load in constant time. As an application, we consider the following problem. Given a fully connected graph of n nodes, where each node needs to send and receive up to n messages, and in each round each node may send one message over each link, deliver all messages as quickly as possible to their destinations. We give a simple and robust algorithm of time complexity O(log* n) for this task and provide a generalization to the case where all nodes initially hold arbitrary sets of messages. A less practical algorithm terminates within asymptotically optimal O(1) rounds. All these bounds hold with high probability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
