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Rank position forecasting in car racing is a challenging problem when using a Deep Learning-based model over timeseries data. It is featured with highly complex global dependency among the racing cars, with uncertainty resulted from existing and external factors; and it is also a problem with data scarcity. Existing methods, including statistical models, machine learning regression models, and several state-of-the-art deep forecasting models all perform not well on this problem. By an elaborate analysis of pit stop events, we find it critical to decompose the cause-and-effect relationship and model the rank position and pit stop events separately. In choosing a sub-model from different neural network models, we find the model with weak assumptions on the global dependency structure performs the best. Based on these observations, we propose RankNet, a combination of the encoder-decoder network and a separate Multilayer Perception network that is capable of delivering probabilistic forecasting to model the pit stop events and rank position in car racing. Further with the help of feature optimizations, RankNet demonstrates a significant performance improvement, where MAE improves 19% in two laps forecasting task and 7% in the stint forecasting task over the best baseline and is also more stable when adapting to unseen new data. Details of the model optimizations and performance profiling are presented. It is promising to provide useful interactions of neural networks in forecasting racing cars and shine a light on solutions to similar challenging issues in general forecasting problems. 

Several variants of the subgraph isomorphism problem, e.g., finding, counting and estimating frequencies of subgraphs in networks arise in a number of real world applications, such as web analysis, disease diffusion prediction and social network analysis. These problems are computationally challenging in having to scale to very large networks with millions of vertices. In this paper, we present SAHAD, a MapReduce algorithm for detecting and counting trees of bounded size using the elegant color coding technique developed by N. Alon et al. SAHAD is a randomized algorithm, and we show rigorous bounds on the approximation quality and the performance of it. SAHAD scales to very large networks comprising of 107-108 edges and tree-like (acyclic) templates with up to 12 vertices. Further, we extend our results by implementing SAHAD in the Harp framework, which is more of a high performance computing environment. The new implementation gives 100x improvement in performance over the standard Hadoop implementation and achieves better performance than state-of-the-art MPI solutions on larger graphs.