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.Comment: 28 pages, 7 figures, 10 tables, 2 algorithms. arXiv admin note: substantial text overlap with arXiv:1209.581

Towards Business Partnership Recommendation Using User Opinion on Facebook

The identification of strategic business partnerships can potentially provide competitive advantages for businesses; however, due to the dynamics and uncertainty present in business environments, this task could be challenging. To help businesses in this task, this study presents a similarity model between businesses that consider the opinions of users on content shared by businesses on social media. Thus, this model captures significant virtual relationships among businesses that are generated by users in the virtual world. Besides, we propose an algorithm for detecting business communities in the considered model. We also propose an algorithm to identify possible business outliers in the detected communities, which could represent an automatic way to identify non-obvious relations that might deserve particular attention of business owners. By exploring approximately 280 million user reactions on Facebook, we show that our results could favor the development of, for example, a new strategic business partnership recommendation service