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Graph algorithms are becoming increasingly important for analyzing large datasets in many fields. Real-world graph data follows a pattern of sparsity, that is not uniform but highly skewed towards a few items. Implementing graph traversal, statistics and machine learning algorithms on such data in a scalable manner is quite challenging. As a result, several graph analytics frameworks (GraphLab, CombBLAS, Giraph, SociaLite and Galois among others) have been developed, each offering a solution with different programming models and targeted at different users. Unfortunately, the "Ninja performance gap" between optimized code and most of these frameworks is very large (2-30X for most frameworks and up to 560X for Giraph) for common graph algorithms, and moreover varies widely with algorithms. This makes the end-users' choice of graph framework dependent not only on ease of use but also on performance. In this work, we offer a quantitative roadmap for improving the performance of all these frameworks and bridging the "ninja gap". We first present hand-optimized baselines that get performance close to hardware limits and higher than any published performance figure for these graph algorithms. We characterize the performance of both this native implementation as well as popular graph frameworks on a variety of algorithms. This study helps endusers delineate bottlenecks arising from the algorithms themselves vs. programming model abstractions vs. the framework implementations. Further, by analyzing the system-level behavior of these frameworks, we obtain bottlenecks that are agnostic to specific algorithms. We recommend changes to alleviate these bottlenecks (and implement some of them) and reduce the performance gap with respect to native code. These changes will enable end-users to choose frameworks based mostly on ease of use.

Abstract. The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs. We present a new exact algorithm that employs novel pruning techniques and is able to quickly find maximum cliques in large sparse graphs. Extensive experiments on different kinds of synthetic and real-world graphs show that our new algorithm can be orders of magnitude faster than existing algorithms. We also present a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions.

Abstract-DBSCAN is a well-known density based clustering algorithm capable of discovering arbitrary shaped clusters and eliminating noise data. However, parallelization of DBSCAN is challenging as it exhibits an inherent sequential data access order. Moreover, existing parallel implementations adopt a master-slave strategy which can easily cause an unbalanced workload and hence result in low parallel efficiency.We present a new parallel DBSCAN algorithm (PDSDBSCAN) using graph algorithmic concepts. More specifically, we employ the disjoint-set data structure to break the access sequentiality of DBSCAN. In addition, we use a tree-based bottom-up approach to construct the clusters. This yields a better-balanced workload distribution. We implement the algorithm both for shared and for distributed memory.Using data sets containing up to several hundred million high-dimensional points, we show that PDSDBSCAN significantly outperforms the master-slave approach, achieving speedups up to 25.97 using 40 cores on shared memory architecture, and speedups up to 5,765 using 8,192 cores on distributed memory architecture.

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. Despite clique's status as an NP-hard problem with poor approximation guarantees, our method exhibits nearly linear runtime scaling over realworld networks ranging from 1000 to 100 million nodes. In a test on a social network with 1.8 billion edges, the algorithm finds the largest clique in about 20 minutes. Key to the efficiency of our algorithm are an initial heuristic procedure that finds a large clique quickly and a parallelized branch and bound strategy with aggressive pruning and ordering techniques. We use the algorithm to compute the largest temporal strong components of temporal contact networks.We propose a fast, parallel maximum clique finder wellsuited for applications involving large sparse graphs. Our algorithm is a branch and bound method with novel and aggressive pruning strategies. Branch and bound type algorithms for maximum clique explore all maximal cliques that cannot be pruned via search tree optimizations [3,7,5,8]. They differ chiefly in the way the pruning is done. Our algorithm is distinguished by several features. First, it begins by finding a large clique using a near linear-time heuristic; the obtained solution is checked for optimality before the algorithm proceeds any further, and the algorithm is terminated if the solution is found to be optimal. Second, we use this heuristic clique, in combination with (tight) upper bounds on the largest clique, to aggressively prune. The upper bounds are computed at the level of the input graph or individual neighborhoods. Third, we use implicit graph edits and periodic full graph updates in order to keep our

We present new multi-core algorithms for computing spanning forests and connected components of large sparse graphs. The algorithms are based on the use of the disjoint-set data structure. When compared with the previous best algorithms for these problems our algorithms are appealing for several reasons: Extensive experiments using up to 40 threads on several different types of graphs show that they scale better. Also, the new algorithms do not make use of any hardware specific routines, and thus are highly portable. Finally, the algorithms are quite simple and easy to implement.

The maximum clique problem is a well-known NP-hard problem with applications in data mining, network analysis, information retrieval, and many other areas related to the World Wide Web. There exist several algorithms for the problem, with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs. We present a new exact algorithm that employs novel pruning techniques and is able to find maximum cliques in very large, sparse graphs quickly. Extensive experiments on different kinds of synthetic and real-world graphs show that our new algorithm can be orders of magnitude faster than existing algorithms. We also present a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions. We illustrate a simple application of the algorithms in developing methods for detection of overlapping communities in networks.

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