一种实用的线性时间全分布式不规则聚散算法
Practical, Linear-time, Fully Distributed Algorithms for Irregular Gather and Scatter
摘要：
我们提出了新的，简单的，完全分布式的，实用的算法与线性时间通信成本不规则的收集和分散操作中，处理器的贡献或消耗可能不同的数据量。在具有启动延迟$α$和单位成本$β$的线性成本传输模型中，新算法花费时间$3|{\log_2 p}|α+β\sum_{i\neq r}m_i$，其中$p$是处理器的数量，$m_i$是处理器$i, 0\leq i<p$的数据量，处理器$r, 0\leq r<p$是由算法确定的根处理器。对于固定的、外部给定的根处理器$r$，存在至多$β(M_{d'}-m_{r_{d'}}-\sum_{0\leq j<d'}M_j)$时间步的附加惩罚，其中每个$M_j$是由该算法构造的具有根$r_j$的$2^j$不同处理器的树中的数据总量。最差情况的惩罚小于$β\sum_{i\neq r}m_i$时间步长。该算法具有实现MPI（消息传递接口）的操作有吸引力的属性。使用固定树的标准算法在最坏的情况下花费$|{\log_2 p}|(α+β\sum_{i\neq r} m_i)$时间，或者花费$\sum_{i\neq r}(α+βm_i)$时间。我们已经使用了新的算法，给出原型实现的MPI_Gatherv和MPI_Scatterv集体的MPI，并提出了基准测试结果从一个小型和中型的InfiniBand集群。为了构建实验评价，我们制定了新的性能准则，不规则的集体，可以用来评估相应的定期集体的性能。我们表明，新的算法可以满足这些性能的期望，有很大的利润，而标准的实现不。
英文摘要：
We present new, simple, fully distributed, practical algorithms with linear time communication cost for irregular gather and scatter operations in which processors contribute or consume possibly different amounts of data. In a linear cost transmission model with start-up latency $α$ and cost per unit $β$, the new algorithms take time $3|{\log_2 p}|α+β\sum_{i\neq r}m_i$ where $p$ is the number of processors, $m_i$ the amount of data for processor $i, 0\leq i<p$, and processor $r, 0\leq r<p$ a root processor determined by the algorithm. For a fixed, externally given root processor $r$, there is an additive penalty of at most $β(M_{d'}-m_{r_{d'}}-\sum_{0\leq j<d'}M_j)$ time steps where each $M_j$ is the total amount of data in a tree of $2^j$ different processors with roots $r_j$ as constructed by the algorithm. The worst-case penalty is less than $β\sum_{i\neq r}m_i$ time steps. The algorithms have attractive properties for implementing the operations for MPI (the Message-Passing Interface). Standard algorithms using fixed trees take time either $|{\log_2 p}|(α+β\sum_{i\neq r} m_i)$ in the worst case, or $\sum_{i\neq r}(α+βm_i)$. We have used the new algorithms to give prototype implementations for the MPI_Gatherv and MPI_Scatterv collectives of MPI, and present benchmark results from a small and a medium-large InfiniBand cluster. In order to structure the experimental evaluation we formulate new performance guidelines for irregular collectives that can be used to assess the performance in relation to the corresponding regular collectives. We show that the new algorithms can fulfill these performance expectations with a large margin, and that standard implementations do not.
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。
