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

Dynamic Power Splitting Policies for AF Relay Networks with Wireless Energy Harvesting

Wireless energy harvesting (WEH) provides an exciting way to supply energy for relay nodes to forward information for the source-destination pairs. In this paper, we investigate the problem on how the relay node dynamically adjusts the power splitting ratio of information transmission (IT) and energy harvesting (EH) in order to achieve the optimal outage performance. According to the knowledge of channel state information (CSI) at the relay, optimal dynamic power splitting policy with full CSI and partial CSI are both provided. Finally, through simulations, the proposed power splitting policies can improve the outage performances and the policy with full CSI achieves the best performance. It is also shown that the policy with partial CSI can approach the policy with full CSI closely and incurs far less system overhead.Comment: accepted by IEEE ICC 2015 - Workshop on Green Communications and Networks with Energy Harvesting, Smart Grids, and Renewable Energie

Greedy Strategy Works for k-Center Clustering with Outliers and Coreset Construction

We study the problem of k-center clustering with outliers in arbitrary metrics and Euclidean space. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez\u27s algorithm, for solving the problem of ordinary k-center clustering. Based on some novel observations, we show that this greedy strategy actually can handle k-center clustering with outliers efficiently, in terms of clustering quality and time complexity. We further show that the greedy approach yields small coreset for the problem in doubling metrics, so as to reduce the time complexity significantly. Our algorithms are easy to implement in practice. We test our method on both synthetic and real datasets. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower running times comparing with existing methods