Improved Algorithms for Time Decay Streams

In the time-decay model for data streams, elements of an underlying data set arrive sequentially with the recently arrived elements being more important. A common approach for handling large data sets is to maintain a coreset, a succinct summary of the processed data that allows approximate recovery of a predetermined query. We provide a general framework that takes any offline-coreset and gives a time-decay coreset for polynomial time decay functions. We also consider the exponential time decay model for k-median clustering, where we provide a constant factor approximation algorithm that utilizes the online facility location algorithm. Our algorithm stores O(k log(h Delta)+h) points where h is the half-life of the decay function and Delta is the aspect ratio of the dataset. Our techniques extend to k-means clustering and M-estimators as well

Efficient representative subset selection over sliding windows

Representative subset selection (RSS) is an important tool for users to draw insights from massive datasets. Existing literature models RSS as the submodular maximization problem to capture the "diminishing returns" property of the representativeness of selected subsets, but often only has a single constraint (e.g., cardinality), which limits its applications in many real-world problems. To capture the data recency issue and support different types of constraints, we formulate dynamic RSS in data streams as maximizing submodular functions subject to general $d$-knapsack constraints (SMDK) over sliding windows. We propose a \textsc{KnapWindow} framework (KW) for SMDK. KW utilizes the \textsc{KnapStream} algorithm (KS) for SMDK in append-only streams as a subroutine. It maintains a sequence of checkpoints and KS instances over the sliding window. Theoretically, KW is $\frac{1-\varepsilon}{1+d}$-approximate for SMDK. Furthermore, we propose a \textsc{KnapWindowPlus} framework (KW$^{+}$) to improve upon KW. KW$^{+}$ builds an index \textsc{SubKnapChk} to manage the checkpoints and KS instances. \textsc{SubKnapChk} deletes a checkpoint whenever it can be approximated by its successors. By keeping much fewer checkpoints, KW$^{+}$ achieves higher efficiency than KW while still guaranteeing a $\frac{1-\varepsilon'}{2+2d}$-approximate solution for SMDK. Finally, we evaluate the efficiency and solution quality of KW and KW$^{+}$ in real-world datasets. The experimental results demonstrate that KW achieves more than two orders of magnitude speedups over the batch baseline and preserves high-quality solutions for SMDK over sliding windows. KW$^{+}$ further runs 5-10 times faster than KW while providing solutions with equivalent or even better utilities.Comment: 26 pages, 9 figures, to appear in IEEE Transactions on Knowledge and Data Engineering (TKDE). 201

Real-time influence maximization on dynamic social streams

Influence maximization (IM), which selects a set of $k$ users (called seeds) to maximize the influence spread over a social network, is a fundamental problem in a wide range of applications such as viral marketing and network monitoring. Existing IM solutions fail to consider the highly dynamic nature of social influence, which results in either poor seed qualities or long processing time when the network evolves. To address this problem, we define a novel IM query named Stream Influence Maximization (SIM) on social streams. Technically, SIM adopts the sliding window model and maintains a set of $k$ seeds with the largest influence value over the most recent social actions. Next, we propose the Influential Checkpoints (IC) framework to facilitate continuous SIM query processing. The IC framework creates a checkpoint for each window slide and ensures an $\varepsilon$-approximate solution. To improve its efficiency, we further devise a Sparse Influential Checkpoints (SIC) framework which selectively keeps $O(\frac{\log{N}}{\beta})$ checkpoints for a sliding window of size $N$ and maintains an $\frac{\varepsilon(1-\beta)}{2}$-approximate solution. Experimental results on both real-world and synthetic datasets confirm the effectiveness and efficiency of our proposed frameworks against the state-of-the-art IM approaches.Comment: An extended version of VLDB 2017 paper "Real-Time Influence Maximization on Dynamic Social Streams", 14 page