Identifying influential nodes that can jointly trigger the maximum influence spread in networks is a fundamental problem in many applications such as viral marketing, online advertising, and disease control. Most existing studies assume that social influence is static and they fail to capture the dynamics of influence in reality. In this work, we address the dynamic influence challenge by designing efficient streaming methods that can identify influential nodes from highly dynamic node interaction streams. We first propose a general time-decaying dynamic interaction network (TDN) model to model node interaction streams with the ability to smoothly discard outdated data. Based on the TDN model, we design three algorithms, i.e., SieveADN, BasicReduction, and HistApprox. SieveADN identifies influential nodes from a special kind of TDNs with efficiency. BasicReduction uses SieveADN as a basic building block to identify influential nodes from general TDNs. HistApprox significantly improves the efficiency of BasicReduction. More importantly, we theoretically show that all three algorithms enjoy constant factor approximation guarantees. Experiments conducted on various real interaction datasets demonstrate that our approach finds near-optimal solutions with speed at least @math to @math times faster than baseline methods.
The sliding-window stream model is first introduced in @cite_25 for maintaining summation aggregates on a data stream (e.g., counting the number of @math 's in a @math - @math stream). @cite_9 leverage the smooth histogram technique @cite_14 to solve SSO under the sliding-window stream, and achieves a @math approximation factor. @cite_4 further improve the approximation factor to @math .
@cite_9 @cite_14 @cite_4 @cite_25
2547615739 2128846062 2004110412
In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent data, and study the maximization problem over sliding windows. We provide a general reduction from the sliding window model to the standard streaming model, and thus our approach works for general constraints as long as there is a corresponding streaming algorithm in the standard streaming model. As a consequence, we obtain the first algorithms in the sliding window model for maximizing a monotone non-monotone submodular function under cardinality and matroid constraints. We also propose several heuristics and show their efficiency in real-world datasets. In the streaming model elements arrive sequentially and can be observed only once. Maintaining statistics and aggregates is an important and non-trivial task in the model. This becomes even more challenging in the sliding windows model, where statistics must be maintained only over the most recent n elements. In their pioneering paper, Datar, Gionis, Indyk and Motwani [15] presented exponential histograms, an effective method for estimating statistics on sliding windows. In this paper we present a new smooth histograms method that improves the approximation error rate obtained via exponential histograms. Furthermore, our smooth histograms method not only captures and improves multiple previous results on sliding windows bur also extends the class functions that can be approximated on sliding windows. In particular, we provide the first approximation algorithms for the following functions: Lp norms for p notin [1,2], frequency moments, length of increasing subsequence and geometric mean. We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's in the last N elements seen from the stream. We show that, using @math bits of memory, we can estimate the number of 1's to within a factor of @math . We also give a matching lower bound of @math memory bits for any deterministic or randomized algorithms. We extend our scheme to maintain the sum of the last N positive integers and provide matching upper and lower bounds for this more general problem as well. We also show how to efficiently compute the Lp norms ( @math ) of vectors in the sliding window model using our techniques. Using our algorithm, one can adapt many other techniques to work for the sliding window model with a multiplicative overhead of @math in memory and a @math factor loss in accuracy. These include maintaining approximate histograms, hash tables, and statistics or aggregates such as sum and averages.