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The closest pair problem (CPP) is one of the well studied and fundamentalproblems in computing. Given a set of points in a metric space, the problem isto identify the pair of closest points. Another closely related problem is thefixed radius nearest neighbors problem (FRNNP). Given a set of points and aradius $R$, the problem is, for every input point $p$, to identify all theother input points that are within a distance of $R$ from $p$. A naivedeterministic algorithm can solve these problems in quadratic time. CPP as wellas FRNNP play a vital role in computational biology, computational finance,share market analysis, weather prediction, entomology, electro cardiograph,N-body simulations, molecular simulations, etc. As a result, any improvementsmade in solving CPP and FRNNP will have immediate implications for the solutionof numerous problems in these domains. We live in an era of big data andprocessing these data take large amounts of time. Speeding up data processingalgorithms is thus much more essential now than ever before. In this paper wepresent algorithms for CPP and FRNNP that improve (in theory and/or practice)the best-known algorithms reported in the literature for CPP and FRNNP. Thesealgorithms also improve the best-known algorithms for related applicationsincluding time series motif mining and the two locus problem in Genome WideAssociation Studies (GWAS).

Efficient Algorithms for the Closest Pair Problem and Applications