You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other clusters. In the context of a social network, a cluster could be a group of friends. Modularity and map equation are established formalizations of this internally-dense-externally-sparse principle. We present two versions of a simple distributed algorithm to optimize both measures. They are based on Thrill, a distributed big data processing framework that implements an extended MapReduce model. The algorithms for the two measures, DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality measures is straight-forward. We conduct an extensive experimental study on real-world graphs and on synthetic benchmark graphs with up to 68 billion edges. Our algorithms are fast while detecting clusterings similar to those detected by other sequential, parallel and distributed clustering algorithms. Compared to the distributed GossipMap algorithm, DSLM-Map needs less memory, is up to an order of magnitude faster and achieves better quality.

Cited Abstract(s):
[1]: In pursuit of graph processing performance, the systems community has largely abandoned general-purpose distributed dataflow frameworks in favor of specialized graph processing systems that provide tailored programming abstractions and accelerate the execution of iterative graph algorithms. In this paper we argue that many of the advantages of specialized graph processing systems can be recovered in a modern general-purpose distributed dataflow system. We introduce GraphX, an embedded graph processing framework built on top of Apache Spark, a widely used distributed dataflow system. GraphX presents a familiar composable graph abstraction that is sufficient to express existing graph APIs, yet can be implemented using only a few basic dataflow operators (e.g., join, map, group-by). To achieve performance parity with specialized graph systems, GraphX recasts graph-specific optimizations as distributed join optimizations and materialized view maintenance. By leveraging advances in distributed dataflow frameworks, GraphX brings low-cost fault tolerance to graph processing. We evaluate GraphX on real workloads and demonstrate that GraphX achieves an order of magnitude performance gain over the base dataflow framework and matches the performance of specialized graph processing systems while enabling a wider range of computation.

[2]: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.

[3]: Identification of different communities in large weighted networks is of crucial importance since it helps to uncover priori unknown functional modules such as topics in information networks or cyber-communities in social networks. However, the typical size of networks, such as social network services or World Wide Web, now counts in millions of nodes and is computationally complex. This urgently demands feasible methods and available computing platforms to retrieve their structure efficiently. To address this problem, we propose an algorithm Fast Community Detection (FastCD) based on modularity optimization. Furthermore, FastCD easily supports parallel computation. We implement FastCD with GraphX, which is an embedded graph processing framework built on top of Apache Spark. After carrying out comprehensive experiments in a 16-nodes cluster (32 vCPU) on Amazon EC2, the results indicate that FastCD not only outperforms the state-of-the-art algorithms in terms of computation time, but also guarantees the accuracy of the solutions under different real-world networks commonly used for efficiency comparison.

[4]: In this paper, we describe a new distributed community detection algorithm for billion-edge directed graphs that, unlike modularity-based methods, achieves cluster quality on par with the best-known algorithms in the literature. We show that a simple approximation to the best-known serial algorithm dramatically reduces computation and enables distributed evaluation yet incurs only a very small impact on cluster quality. We present three main results: First, we show that the clustering produced by our scalable approximate algorithm compares favorably with prior results on small synthetic benchmarks and small real-world datasets (70 million edges). Second, we evaluate our algorithm on billion-edge directed graphs (a 1.5B edge social network graph, and a 3.7B edge web crawl), and show that the results exhibit the structural properties predicted by analysis of much smaller graphs from similar sources. Third, we show that our algorithm exhibits over 90 parallel efficiency on massive graphs in weak scaling experiments.
The second approach consists of distributing the clustering algorithm itself. Using MPI, [1] have introduced a distributed extension of the Louvain algorithm [2] . Similarly, [3] have presented an algorithm that uses the GraphX framework. Another algorithm named GossipMap is presented in [4] which uses the GraphLab framework. Our algorithms also use this second approach.