Graph visualization is a vital component in many real-world applications (e.g., social network analysis, web mining, and bioinformatics) that enables users to unearth crucial insights from complex data. Lying in the c...
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Graph visualization is a vital component in many real-world applications (e.g., social network analysis, web mining, and bioinformatics) that enables users to unearth crucial insights from complex data. Lying in the core of graph visualization is the node distance measure, which determines how the nodes are placed on the screen. A favorable node distance measure should be informative in reflecting the full structural information between nodes and effective in optimizing visual aesthetics. However, existing node distance measures yield sub-par visualization quality as they fall short of these requirements. Moreover, most existing measures are computationally inefficient, incurring a long response time when visualizing large graphs. To overcome such deficiencies, we propose a new node distance measure, PDist, geared towards graph visualization by exploiting a well-known node proximity measure,personalized PageRank. Moreover, we propose an efficient algorithm Tau-Push for estimating PDist under both single- and multi-level visualization settings. With several carefully-designed techniques, TauPush offers non-trivial theoretical guarantees for estimation accuracy and computation complexity. Extensive experiments show that our proposal significantly outperforms 13 state-of-the-art graph visualization solutions on 12 real-world graphs in terms of both efficiency and effectiveness (including aesthetic criteria and user feedback). In particular, our proposal can interactively produce satisfactory visualizations within one second for billion-edge graphs.
An efficient discovery algorithm of frequently occurring patterns, called motifs, in a time series would be useful as a tool for summarizing and visualizing big time series databases. In this paper, we propose an effi...
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An efficient discovery algorithm of frequently occurring patterns, called motifs, in a time series would be useful as a tool for summarizing and visualizing big time series databases. In this paper, we propose an efficient approximate algorithm, called DiscMotifs, to discover the K most significant ( KMS ) motifs from time series. First, the proposed algorithm transforms the time series into a SAX representation and then the algorithm divides the SAX representation into subsequences. Next, these subsequences are linearized by projecting them into a one-dimensional space based on their distances form a randomly selected reference point, or a subsequence. By utilizing the linear ordering of subsequences, DiscMotifs efficiently discovers the KMS motifs. DiscMotifs algorithm requires a storage space linear to the number of subsequences. We demonstrate the feasibility of this approach on several synthetic and real application datasets.
Any real world system must have at least one constraint to limit the system from achieving its objective. How to make good use of constraints is of vital importance to increase the efficiency of the system. In this pa...
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Any real world system must have at least one constraint to limit the system from achieving its objective. How to make good use of constraints is of vital importance to increase the efficiency of the system. In this paper, an approximate algorithm consisting of two stages of approaches is proposed for solving the real world problems. The first stage of approach called Basic Approach (BA) is proposed for searching a suboptimal solution with non-relaxing resources. The second stage of approach called Buffer Management Approach (BMA) is proposed for improving the solution obtained from BA and excluding the situations of violating restrictions by relaxing resources. According to the complicacy, diversity and limited resources of real world problems, an idea of relaxing resources is embedded in the second stage of approach. The methods of Drum-Buffer-Rope (DBR) scheduling and buffer management are used in the approaches for excluding the constraints in the process and increasing the efficiency of the system. The proposed algorithm is applied to solving the Loading Allocation and Scheduling Problems (LASP) in real world. By combining the two stages of approaches, the proposed algorithm is considered to be effective and adaptive for solving a real world problem with complicated restrictions.
Facility Relocation (FR), which is an effort to reallocate the placement of facilities to adapt to the changes of urban planning, has remarkable impact on many areas. Existing solutions fail to guarantee the result qu...
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Facility Relocation (FR), which is an effort to reallocate the placement of facilities to adapt to the changes of urban planning, has remarkable impact on many areas. Existing solutions fail to guarantee the result quality on relocating k > 1 facilities. As k-FR problem is NP-complete and is not submodular or non-decreasing, traditional greedy algorithm cannot be directly applied. We propose to transform k-FR into another facility placement problem, which is submodular and non-decreasing. We prove that the optimal solutions of both problems are equivalent. Accordingly, we present the first approximate solution toward the k-FR, FR2FP. Our extensive comparison over both FR2FP and the state-of-the-art solution shows that FR2FP, although it provides approximation guarantee, cannot necessarily given superior results. The comparison motivates us to present an advanced approximate solution, FR2FP-ex. Moreover, based on Lagrangian relaxation, we develop an algorithm that can adjust the approximation ratio. Extensive experiments verified that, FR2FP-ex demonstrates the best result quality, and it is very close to the optimal solution. In addition, we also unveil the scenarios when the state-of-the-art would fail. We further generalize the k-FR problem, considering the budget for relocation and the cost of each facility. We also present corresponding approximate solutions toward the new problem and prove the approximation ratio.
K -best enumeration , which asks to output k -best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been...
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K -best enumeration , which asks to output k -best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much attention to such fields. However, k -best enumeration tends to be intractable since, in many cases, finding one optimum solution is NP -hard. To overcome this difficulty, we combine k -best enumeration with a concept of enumeration algorithms called approximation enumeration algorithms . As a main result, we propose a 4 -approximation algorithm for minima l con nected edge dominating sets which outputs k minimal solutions with cardinality at most 4 & sdot;OPT, where OPT is the cardinality of a minimum solution which is not outputted by the algorithm. Our proposed algorithm runs in O(nm 2 Delta) delay, where n, m, Delta are the number of vertices, the number of edges, and the maximum degree of an input graph.
The so-called Maximum Clique Problem is one of the most famous NP-complete problems for which it is difficult to find a solution. Given an indirected graph, we present here a polynomial-time randomized algorithm RaCLI...
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The so-called Maximum Clique Problem is one of the most famous NP-complete problems for which it is difficult to find a solution. Given an indirected graph, we present here a polynomial-time randomized algorithm RaCLIQUE for finding a near-maximum clique. While the basic idea of the algorithm comes from Boltzmann machines, it employs no simulated annealing at all and hence it is simple to control its execution. We have confirmed in experiments for several random and nonrandom graphs with up to 400 nodes that very good solutions can be found efficiently compared with the other conventional algorithms.
In wireless powered communication networks (WPCNs), the harvested energy varies greatly among user nodes (UNs), resulting in throughput unfairness. Since the harvested energy is limited, each UN must strategically all...
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In wireless powered communication networks (WPCNs), the harvested energy varies greatly among user nodes (UNs), resulting in throughput unfairness. Since the harvested energy is limited, each UN must strategically allocate the energy used for forwarding the other nodes' information and for transmitting its own information, which further aggravates the global unfairness in terms of throughput. In this paper, we leverage user cooperation in multi-hop transmission to improve the throughput fairness. We formulate the fairness problem as the max-min throughput with resource allocation, which is NP-hard. We design an approximate algorithm to address this problem. The theoretical proof and the simulation results both show that the proposed algorithm provides tight upper and lower bounds for the optimal solution. Compared with the benchmark methods, our proposed method significantly enhances the throughput fairness for WPCNs.
We present a simple approximate algorithm to compute the Minimum Enclosing Ball (MEB) of training samples in high dimensional Euclidean space. We prove theoretically that the proposed algorithm converges to the optimu...
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We present a simple approximate algorithm to compute the Minimum Enclosing Ball (MEB) of training samples in high dimensional Euclidean space. We prove theoretically that the proposed algorithm converges to the optimum within any precision quickly. Compared to popular MEB algorithms, it has the competitive performances on both training time and accuracy. Besides, the proposed algorithm does not need any extra requirement on kernels, it can be linked with extensive kernel methods, consequently. We also use the proposed algorithm to handle Binary Classification, Multi-class Classification, and Image Clustering problems. Experiments on both synthetic and real-world data sets demonstrate the validity of the algorithm we proposed.
In the process of spectral segmentation, it is crucial to compute a reliable affinity matrix with different features of an image. In this paper, we present a method of constructing the affinity matrix based on multi-r...
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In the process of spectral segmentation, it is crucial to compute a reliable affinity matrix with different features of an image. In this paper, we present a method of constructing the affinity matrix based on multi-resolution features extracted from the original features. A pointwise multi-resolution feature descriptor (PMFD) is designed based on spectral graph wavelets, which characterize the topology of the image centered at different pixels. After choosing the scales of interest in our descriptor, a new affinity matrix is constructed based on the extracted features. For large-size affinity matrixes, it is difficult to compute the proposed PMFD for all pixels of an image. Therefore, an approximate algorithm is proposed to compute the PMFD. To demonstrate the effectiveness of our method, a series of experiments on the Berkeley image segmentation dataset are implemented using the PMFD-based spectral segmentation algorithm. A comparison with other image segmentation techniques demonstrates that our method offers significantly improved pointwise spectral segmentation performance.
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