An Elegant Algorithm for the Construction of Suffix Arrays

The suffix array is a data structure that finds numerous applications in string processing problems for both linguistic texts and biological data. It has been introduced as a memory efficient alternative for suffix trees. The suffix array consists of the sorted suffixes of a string. There are several linear time suffix array construction algorithms (SACAs) known in the literature. However, one of the fastest algorithms in practice has a worst case run time of $O(n^2)$. The problem of designing practically and theoretically efficient techniques remains open. In this paper we present an elegant algorithm for suffix array construction which takes linear time with high probability; the probability is on the space of all possible inputs. Our algorithm is one of the simplest of the known SACAs and it opens up a new dimension of suffix array construction that has not been explored until now. Our algorithm is easily parallelizable. We offer parallel implementations on various parallel models of computing. We prove a lemma on the $\ell$-mers of a random string which might find independent applications. We also present another algorithm that utilizes the above algorithm. This algorithm is called RadixSA and has a worst case run time of $O(n\log{n})$. RadixSA introduces an idea that may find independent applications as a speedup technique for other SACAs. An empirical comparison of RadixSA with other algorithms on various datasets reveals that our algorithm is one of the fastest algorithms to date. The C++ source code is freely available at http://www.engr.uconn.edu/~man09004/radixSA.zi

When Hashing Met Matching: Efficient Spatio-Temporal Search for Ridesharing

Carpooling, or sharing a ride with other passengers, holds immense potential for urban transportation. Ridesharing platforms enable such sharing of rides using real-time data. Finding ride matches in real-time at urban scale is a difficult combinatorial optimization task and mostly heuristic approaches are applied. In this work, we mathematically model the problem as that of finding near-neighbors and devise a novel efficient spatio-temporal search algorithm based on the theory of locality sensitive hashing for Maximum Inner Product Search (MIPS). The proposed algorithm can find $k$ near-optimal potential matches for every ride from a pool of $n$ rides in time $O(n^{1 + \rho} (k + \log n) \log k)$ and space $O(n^{1 + \rho} \log k)$ for a small $\rho < 1$. Our algorithm can be extended in several useful and interesting ways increasing its practical appeal. Experiments with large NY yellow taxi trip datasets show that our algorithm consistently outperforms state-of-the-art heuristic methods thereby proving its practical applicability

Coding for Random Projections

The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which determines the number of bits needed for each projected value and how to allocate these bits, can significantly improve the effectiveness of the algorithm, in storage cost as well as computational speed. In this paper, we study a number of simple coding schemes, focusing on the task of similarity estimation and on an application to training linear classifiers. We demonstrate that uniform quantization outperforms the standard existing influential method (Datar et. al. 2004). Indeed, we argue that in many cases coding with just a small number of bits suffices. Furthermore, we also develop a non-uniform 2-bit coding scheme that generally performs well in practice, as confirmed by our experiments on training linear support vector machines (SVM)

Contextual Motifs: Increasing the Utility of Motifs using Contextual Data

Motifs are a powerful tool for analyzing physiological waveform data. Standard motif methods, however, ignore important contextual information (e.g., what the patient was doing at the time the data were collected). We hypothesize that these additional contextual data could increase the utility of motifs. Thus, we propose an extension to motifs, contextual motifs, that incorporates context. Recognizing that, oftentimes, context may be unobserved or unavailable, we focus on methods to jointly infer motifs and context. Applied to both simulated and real physiological data, our proposed approach improves upon existing motif methods in terms of the discriminative utility of the discovered motifs. In particular, we discovered contextual motifs in continuous glucose monitor (CGM) data collected from patients with type 1 diabetes. Compared to their contextless counterparts, these contextual motifs led to better predictions of hypo- and hyperglycemic events. Our results suggest that even when inferred, context is useful in both a long- and short-term prediction horizon when processing and interpreting physiological waveform data.Comment: 10 pages, 7 figures, accepted for oral presentation at KDD '1

Multiple Methods for Genome Filtering

Filters are fast algorithms, which help to preprocess DNA sequences in order to reduce the time and complexity of approximate motif search. Multiple filtering methods exist, and this paper classifies the filtering algorithms based on their approach, numerical analysis or digital signal processing, and it briefly reviews both classes of filters. The paper also reflects on filters currently used in popular software for genomic processing

Parallel random projection using R high performance computing for planted motif search

Motif discovery in DNA sequences is one of the most important issues in bioinformatics. Thus, algorithms for dealing with the problem accurately and quickly have always been the goal of research in bioinformatics. Therefore, this study is intended to modify the random projection algorithm to be implemented on R high performance computing (i.e., the R package pbdMPI). Some steps are needed to achieve this objective, ie preprocessing data, splitting data according to number of batches, modifying and implementing random projection in the pbdMPI package, and then aggregating the results. To validate the proposed approach, some experiments have been conducted. Several benchmarking data were used in this study by sensitivity analysis on number of cores and batches. Experimental results show that computational cost can be reduced, which is that the computation cost of 6 cores is faster around 34 times compared with the standalone mode. Thus, the proposed approach can be used for motif discovery effectively and efficiently