Efficient Approximation Algorithms for Multi-Antennae Largest Weight Data Retrieval

In a mobile network, wireless data broadcast over $m$ channels (frequencies) is a powerful means for distributed dissemination of data to clients who access the channels through multi-antennae equipped on their mobile devices. The $\delta$-antennae largest weight data retrieval ($\delta$ALWDR) problem is to compute a schedule for downloading a subset of data items that has a maximum total weight using $\delta$ antennae in a given time interval. In this paper, we propose a ratio $1-\frac{1}{e}-\epsilon$ approximation algorithm for the $\delta$-antennae largest weight data retrieval ($\delta$ALWDR) problem that has the same ratio as the known result but a significantly improved time complexity of $O(2^{\frac{1}{\epsilon}}\frac{1}{\epsilon}m^{7}T^{3.5}L)$ from $O(\epsilon^{3.5}m^{\frac{3.5}{\epsilon}}T^{3.5}L)$ when $\delta=1$ \cite{lu2014data}. To our knowledge, our algorithm represents the first ratio $1-\frac{1}{e}-\epsilon$ approximation solution to $\delta$ALWDR for the general case of arbitrary $\delta$. To achieve this, we first give a ratio $1-\frac{1}{e}$ algorithm for the $\gamma$-separated $\delta$ALWDR ($\delta$A$\gamma$LWDR) with runtime $O(m^{7}T^{3.5}L)$, under the assumption that every data item appears at most once in each segment of $\delta$A$\gamma$LWDR, for any input of maximum length $L$ on $m$ channels in $T$ time slots. Then, we show that we can retain the same ratio for $\delta$A$\gamma$LWDR without this assumption at the cost of increased time complexity to $O(2^{\gamma}m^{7}T^{3.5}L)$. This result immediately yields an approximation solution of same ratio and time complexity for $\delta$ALWDR, presenting a significant improvement of the known time complexity of ratio $1-\frac{1}{e}-\epsilon$ approximation to the problem

Identification of functionally related enzymes by learning-to-rank methods

Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a given query, the search operation results in a ranking of the enzymes in the database, from very similar to dissimilar enzymes, while information about the biological function of annotated database enzymes is ignored. In this work we show that rankings of that kind can be substantially improved by applying kernel-based learning algorithms. This approach enables the detection of statistical dependencies between similarities of the active cleft and the biological function of annotated enzymes. This is in contrast to search-based approaches, which do not take annotated training data into account. Similarity measures based on the active cleft are known to outperform sequence-based or structure-based measures under certain conditions. We consider the Enzyme Commission (EC) classification hierarchy for obtaining annotated enzymes during the training phase. The results of a set of sizeable experiments indicate a consistent and significant improvement for a set of similarity measures that exploit information about small cavities in the surface of enzymes

On Geometric Alignment in Low Doubling Dimension

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the alignment of geometric patterns in high dimension finds several novel applications, and has attracted more and more attentions. However, the research is still rather limited in terms of algorithms. To the best of our knowledge, most existing approaches for high dimensional alignment are just simple extensions of their counterparts for 2D and 3D cases, and often suffer from the issues such as high complexities. In this paper, we propose an effective framework to compress the high dimensional geometric patterns and approximately preserve the alignment quality. As a consequence, existing alignment approach can be applied to the compressed geometric patterns and thus the time complexity is significantly reduced. Our idea is inspired by the observation that high dimensional data often has a low intrinsic dimension. We adopt the widely used notion "doubling dimension" to measure the extents of our compression and the resulting approximation. Finally, we test our method on both random and real datasets, the experimental results reveal that running the alignment algorithm on compressed patterns can achieve similar qualities, comparing with the results on the original patterns, but the running times (including the times cost for compression) are substantially lower