SURGE: Continuous Detection of Bursty Regions Over a Stream of Spatial Objects

With the proliferation of mobile devices and location-based services, continuous generation of massive volume of streaming spatial objects (i.e., geo-tagged data) opens up new opportunities to address real-world problems by analyzing them. In this paper, we present a novel continuous bursty region detection problem that aims to continuously detect a bursty region of a given size in a specified geographical area from a stream of spatial objects. Specifically, a bursty region shows maximum spike in the number of spatial objects in a given time window. The problem is useful in addressing several real-world challenges such as surge pricing problem in online transportation and disease outbreak detection. To solve the problem, we propose an exact solution and two approximate solutions, and the approximation ratio is $\frac{1-\alpha}{4}$ in terms of the burst score, where $\alpha$ is a parameter to control the burst score. We further extend these solutions to support detection of top-$k$ bursty regions. Extensive experiments with real-world data are conducted to demonstrate the efficiency and effectiveness of our solutions

Efficient Summing over Sliding Windows

This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of {\Omega}(1/{\epsilon} + log W) memory bits for W{\epsilon}-additive approximations is derived. This is followed by an algorithm whose memory consumption is O(1/{\epsilon} + log W) bits, indicating that the algorithm is optimal and that the bound is tight. Next, the more general problem of maintaining a sum of the last W integers, each in the range of {0,1,...,R}, is addressed. The paper shows that approximating the sum within an additive error of RW{\epsilon} can also be done using {\Theta}(1/{\epsilon} + log W) bits for {\epsilon}={\Omega}(1/W). For {\epsilon}=o(1/W), we present a succinct algorithm which uses B(1 + o(1)) bits, where B={\Theta}(Wlog(1/W{\epsilon})) is the derived lower bound. We show that all lower bounds generalize to randomized algorithms as well. All algorithms process new elements and answer queries in O(1) worst-case time.Comment: A shorter version appears in SWAT 201

KV-match: A Subsequence Matching Approach Supporting Normalization and Time Warping [Extended Version]

The volume of time series data has exploded due to the popularity of new applications, such as data center management and IoT. Subsequence matching is a fundamental task in mining time series data. All index-based approaches only consider raw subsequence matching (RSM) and do not support subsequence normalization. UCR Suite can deal with normalized subsequence match problem (NSM), but it needs to scan full time series. In this paper, we propose a novel problem, named constrained normalized subsequence matching problem (cNSM), which adds some constraints to NSM problem. The cNSM problem provides a knob to flexibly control the degree of offset shifting and amplitude scaling, which enables users to build the index to process the query. We propose a new index structure, KV-index, and the matching algorithm, KV-match. With a single index, our approach can support both RSM and cNSM problems under either ED or DTW distance. KV-index is a key-value structure, which can be easily implemented on local files or HBase tables. To support the query of arbitrary lengths, we extend KV-match to KV-match$_{DP}$, which utilizes multiple varied-length indexes to process the query. We conduct extensive experiments on synthetic and real-world datasets. The results verify the effectiveness and efficiency of our approach.Comment: 13 page