Massive volumes of data continuously generated on social platforms have become an important information source for users. A primary method to obtain fresh and valuable information from social streams is . Although there have been extensive studies on social search, existing methods only focus on the of query results but ignore the . In this paper, we propose a novel Semantic and Influence aware @math -Representative ( @math -SIR) query for social streams based on topic modeling. Specifically, we consider that both user queries and elements are represented as vectors in the topic space. A @math -SIR query retrieves a set of @math elements with the maximum over the sliding window at query time w.r.t. the query vector. The representativeness of an element set comprises both semantic and influence scores computed by the topic model. Subsequently, we design two approximation algorithms, namely (MTTS) and (MTTD), to process @math -SIR queries in real-time. Both algorithms leverage the ranked lists maintained on each topic for @math -SIR processing with theoretical guarantees. Extensive experiments on real-world datasets demonstrate the effectiveness of @math -SIR query compared with existing methods as well as the efficiency and scalability of our proposed algorithms for @math -SIR processing.
Submodular maximization has attracted a lot of research interest recently for its theoretical significance and wide applications. The standard approaches to submodular maximization with a cardinality constraint are the greedy heuristic @cite_0 and its improved version CELF @cite_36 , both of which are @math -approximate. Badanidiyuru and Vondrak @cite_27 propose several approximation algorithms for submodular maximization with general constraints. @cite_34 and @cite_12 study the submodular maximization problem in the distributed and streaming settings. @cite_40 and @cite_13 further investigate submodular maximization in the sliding window model. However, the above algorithms do not utilize any indices for acceleration and thus they are much less efficient for processing than and proposed in this paper.
@cite_36 @cite_0 @cite_27 @cite_40 @cite_34 @cite_13 @cite_12
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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. We consider the Unconstrained Submodular Maximization problem in which we are given a nonnegative submodular function @math , and the objective is to find a subset @math maximizing @math . This is one of the most basic submodular optimization problems, having a wide range of applications. Some well-known problems captured by Unconstrained Submodular Maximization include Max-Cut, Max-DiCut, and variants of Max-SAT and maximum facility location. We present a simple randomized linear time algorithm achieving a tight approximation guarantee of 1 2, thus matching the known hardness result of Feige, Mirrokni, and Vondrak [SIAM J. Comput., 40 (2011), pp. 1133--1153]. Our algorithm is based on an adaptation of the greedy approach which exploits certain symmetry properties of the problem. Consider a suboptimal solution S for a maximization problem. Suppose S's value is small compared to an optimal solution OPT to the problem, yet S is structurally similar to OPT. A natural question in this setting is whether there is a way of improving S based solely on this information. In this paper we introduce the Structural Continuous Greedy Algorithm, answering this question affirmatively in the setting of the Nonmonotone Submodular Maximization Problem. We improve on the best approximation factor known for this problem. In the Nonmonotone Submodular Maximization Problem we are given a non-negative submodular function f, and the objective is to find a subset maximizing f. Our method yields an 0.42-approximation for this problem, improving on the current best approximation factor of 0.41 given by Gharan and Vondrak [5]. On the other hand, [4] showed a lower bound of 0.5 for this problem. Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this question in the context of data streams, where elements arrive one at a time, and we want to design low-memory and fast update-time algorithms that maintain a good solution. Specifically, we focus on the sliding window model, where we are asked to maintain a solution that considers only the last W items. In this context, we provide the first non-trivial algorithm that maintains a provable approximation of the optimum using space sublinear in the size of the window. In particular we give a 1 3 - e approximation algorithm that uses space polylogarithmic in the spread of the values of the elements, δ, and linear in the solution size k for any constant e > 0. At the same time, processing each element only requires a polylogarithmic number of evaluations of the function itself. When a better approximation is desired, we show a different algorithm that, at the cost of using more memory, provides a 1 2 - e approximation, and allows a tunable trade-off between average update time and space. This algorithm matches the best known approximation guarantees for submodular optimization in insertion-only streams, a less general formulation of the problem. We demonstrate the efficacy of the algorithms on a number of real world datasets, showing that their practical performance far exceeds the theoretical bounds. The algorithms preserve high quality solutions in streams with millions of items, while storing a negligible fraction of them.