Application-driven graph partitioning

Abstract

Graph partitioning is crucial to parallel computations on large graphs. The choice of partitioning strategies has strong impact on the performance of graph algorithms. For an algorithm of our interest, what partitioning strategy fits it the best and improves its parallel execution? Is it possible to provide a uniform partition to a batch of algorithms that run on the same graph simultaneously, and speed up each and every of them? This paper aims to answer these questions. We propose an application-driven hybrid partitioning strategy that, given a graph algorithm ${{\mathcal {A}}}$, learns a cost model for ${{\mathcal {A}}}$ as polynomial regression. We develop partitioners that, given the learned cost model, refine an edge-cut or vertex-cut partition to a hybrid partition and reduce the parallel cost of ${{\mathcal {A}}}$. Moreover, we extend the cost-driven strategy to support multiple algorithms at the same time and reduce the parallel cost of each of them. Using real-life and synthetic graphs, we experimentally verify that our partitioning strategy improves the performance of a variety of graph algorithms, up to $22.5\times$.

Appendix: More experimental study

1.1 Impact of different phases

We tested the phases of ${\mathsf {ParE2H}}$ and ${\mathsf {ParV2H}}$ for their effectiveness. Denote by ${\mathsf {ParE2H}}_{k}$ (resp. ${\mathsf {ParV2H}}_{k}$) ($1\le k \le 3$) the partitioner with the first k phases of ${\mathsf {ParE2H}}$ (resp. ${\mathsf {ParV2H}}$). We assessed the speedup gain of the kth phase of ${\mathsf {ParE2H}}$ by comparing ${\mathsf {ParE2H}}_{k-1}$ and ${\mathsf {ParE2H}}_{k}$; similarly for ${\mathsf {ParV2H}}$. Figure 11a, b reports the normalized speedup ratio over $\mathsf {Twitter}$ with $n=96$ for $\mathsf {HxtraPuLP}$ and $\mathsf {HGrid}$, respectively. The results over $\mathsf {liveJournal}$ and $\mathsf {UKWeb}$ and other hybrid partitioners are consistent (not shown). We find the following.

• (1) ${\mathsf {ParE2H}}$. (a) Phase ${\mathsf {EMigrate}}$ accounts for 67.5%, 26.3%, 83.5%, 74.4% and $89.2\%$ of the total speedup of $\mathsf {CN}$,  $\mathsf {TC}$, $\mathsf {WCC}$, $\mathsf {PR}$ and $\mathsf {SSSP}$, respectively. (b) ${\mathsf {ESplit}}$ alone improves $\mathsf {CN}$  and $\mathsf {TC}$ by 1.1 and 2.7 times, respectively. For $\mathsf {WCC}$, $\mathsf {PR}$  and $\mathsf {SSSP}$, its impact is smaller, since $\mathsf {CN}$  and $\mathsf {TC}$ are more sensitive to workload imbalance. The impact of ${\mathsf {ESplit}}$ on $\mathsf {CN}$ over $\mathsf {Twitter}$ is smaller, since we filtered large-degree vertices for $\mathsf {CN}$. Without filtering, ${\mathsf {ESplit}}$ improves $\mathsf {CN}$   over $\mathsf {liveJournal}$ by 1.9 times. (c) ${\mathsf {MAssign}}$ accounts for another 22.3, 30.1, 13.8, 21.9 and $6.3\%$ of the speedup of $\mathsf {CN}$,  $\mathsf {TC}$, $\mathsf {WCC}$, $\mathsf {PR}$  and $\mathsf {SSSP}$, respectively.

• (2) ${\mathsf {ParV2H}}$. (a) Phase ${\mathsf {VMigrate}}$ contributes the most to the speedup of $\mathsf {CN}$,  $\mathsf {TC}$, $\mathsf {WCC}$, $\mathsf {PR}$  and $\mathsf {SSSP}$, which account for about 71.2, 81.2, 87.1, 78.2 and $96.7\%$ of the total speedup, respectively. (b) By merging v-cut nodes into e-cut nodes, ${\mathsf {VMerge}}$ contributes 16.5, 5.8, 2.6, 7.1 and 1.2% of the total speedup for the five algorithms tested, respectively. (c) Phase ${\mathsf {MAssign}}$ contributes 9.9% on average.

Fig. 11

Phase decomposition of ${\mathsf {ParE2H}}$ and ${\mathsf {ParV2H}}$