Bharath Pattabiraman

Fast Algorithms for the Maximum Clique Problem on Massive Sparse Graphs

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.

A PARALLEL MONTE CARLO CODE FOR SIMULATING COLLISIONAL N-BODY SYSTEMS

We present a new parallel code for computing the dynamical evolution of collisional N-body systems with up to N ∼ 10 7 particles. Our code is based on the HMonte Carlo method for solving the Fokker-Planck equation, and makes assumptions of spherical symmetry and dynamical equilibrium. The principal algorithmic developments involve optimizing data structures and the introduction of a parallel random number generation scheme as well as a parallel sorting algorithm required to find nearest neighbors for interactions and to compute the gravitational potential. The new algorithms we introduce along with our choice of decomposition scheme minimize communication costs and ensure optimal distribution of data and workload among the processing units. Our implementation uses the Message Passing Interface library for communication, which makes it portable to many different supercomputing architectures. We validate the code by calculating the evolution of clusters with initial Plummer distribution functions up to core collapse with the number of stars, N, spanning three orders of magnitude from 10 5 to 10 7 . We find that our results are in good agreement with self-similar core-collapse solutions, and the core-collapse times generally agree with expectations from the literature. Also, we observe good total energy conservation, within 0.04% throughout all simulations. We analyze the performance of the code, and demonstrate near-linear scaling of the runtime with the number of processors up to 64 processors for N = 10 5 , 128 for N = 10 6 and 256 for N = 10 7 . The runtime reaches saturation with the addition of processors beyond these limits, which is a characteristic of the parallel sorting algorithm. The resulting maximum speedups we achieve are approximately 60×, 100×, and 220×, respectively.

Fast Algorithms for the Maximum Clique Problem on Massive Graphs with Applications to Overlapping Community Detection

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.

Erratum: Binary Black Hole Mergers from Globular Clusters: Implications for Advanced LIGO [Phys. Rev. Lett. 115, 051101 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.115.051101.