45287977
Distance paired-domination problems on subclasses of chordal graphs
Let G=(V,E) be a graph without isolated vertices. For a positive integer k, a set S@?V is a k-distance paired-dominating set if each vertex in V-S is within distance k of a vertex in S and the subgraph induced by S contains a perfect matching. In this paper, we present two linear time algorithms to find a minimum cardinality k-distance paired-dominating set in interval graphs and block graphs, which are two subclasses of chordal graphs. In addition, we present a characterization of trees with unique minimum k-distance paired-dominating set.
33211849
Hardness results and approximation algorithms for (weighted) paired-domination in graphs
Let G=(V,E) be a simple graph without isolated vertices. A vertex set S@?V is a paired-dominating set if every vertex in V-S has a neighbor in S and the induced subgraph G[S] has a perfect matching. In this paper, we investigate the approximation hardness of paired-domination in graphs. For weighted paired-domination, an approximation algorithm in general graphs and an exact dynamic programming style algorithm in trees are also given.
36282948
Extremal problems on consecutive L(2, 1)-labelling
For a given graph G of order n, a k-L(2,1)-labelling is defined as a function f:V(G)->{0,1,2,...,k} such that |f(u)-f(v)|>=2 when d"G(u,v)=1 and |f(u)-f(v)|>=1 when d"G(u,v)=2. The L(2,1)-labelling number of G, denoted by @l(G), is the smallest number k such that G has a k-L(2,1)-labelling. The consecutive L(2,1)-labelling is a variation of L(2,1)-labelling under the condition that the labelling f is an onto function. The consecutive L(2,1)-labelling number of G is denoted by @[email protected]?(G). Obviously, @l(G)=<@[email protected]?(G)=<|V(G)|-1 if G admits a consecutive L(2,1)-labelling. In this paper, we investigate the graphs with @[email protected]?(G)=|V(G)|-1 and the graphs with @[email protected]?(G)[email protected](G), in terms of their sizes, diameters and the number of components.
2641288
A novel spectral coding in a large graph database
Retrieving related graphs containing a query graph from a large graph database is a key issue in many graph-based applications, such as drug discovery and structural pattern recognition. Because sub-graph isomorphism is a NP-complete problem [4], we have to employ a filter-and-verification framework to speed up the search efficiency, that is, using an effective and efficient pruning strategy to filter out the false positives (graphs that are not possible in the results) as many as possible first, then validating the remaining candidates by subgraph isomorphism checking. In this paper, we propose a novel filtering method, a spectral encoding method, i.e. GCoding. Specifically, we assign a signature to each vertex based on its local structures. Then, we generate a spectral graph code by combining all vertex signatures in a graph. Based on spectral graph codes, we derive a necessary condition for sub-graph isomorphism. Then we propose two pruning rules for sub-graph search problem, and prove that they satisfy the no-false-negative requirement (no dismissal in answers). Since graph codes are in numerical space, we take this advantage and conduct efficient filtering over graph codes. Extensive experiments show that GCoding outperforms existing counterpart methods.
2155976
Maximal Subspace Coregulated Gene Clustering
Clustering is a popular technique for analyzing microarray data sets, with n genes and m experimental conditions. As explored by biologists, there is a real need to identify coregulated gene clusters, which include both positive and negative regulated gene clusters. The existing pattern-based and tendency-based clustering approaches cannot directly be applied to find such coregulated gene clusters, because they are designed for finding positive regulated gene clusters. In this paper, in order to cluster coregulated genes, we propose a coding scheme that allows us to cluster two genes into the same cluster if they have the same code, where two genes that have the same code can be either positive or negative regulated. Based on the coding scheme, we propose a new algorithm for finding maximal subspace coregulated gene clusters with new pruning techniques. A maximal subspace coregulated gene cluster clusters a set of genes on a condition sequence such that the cluster is not included in any other subspace coregulated gene clusters. We conduct extensive experimental studies. Our approach can effectively and efficiently find maximal subspace coregulated gene clusters. In addition, our approach outperforms the existing approaches for finding positive regulated gene clusters.
207166969
Probabilistic ranked queries in uncertain databases
Recently, many new applications, such as sensor data monitoring and mobile device tracking, raise up the issue of uncertain data management. Compared to "certain" data, the data in the uncertain database are not exact points, which, instead, often locate within a region. In this paper, we study the ranked queries over uncertain data. In fact, ranked queries have been studied extensively in traditional database literature due to their popularity in many applications, such as decision making, recommendation raising, and data mining tasks. Many proposals have been made in order to improve the efficiency in answering ranked queries. However, the existing approaches are all based on the assumption that the underlying data are exact (or certain). Due to the intrinsic differences between uncertain and certain data, these methods are designed only for ranked queries in certain databases and cannot be applied to uncertain case directly. Motivated by this, we propose novel solutions to speed up the probabilistic ranked query (PRank) over the uncertain database. Specifically, we introduce two effective pruning methods, spatial and probabilistic, to help reduce the PRank search space. Then, we seamlessly integrate these pruning heuristics into the PRank query procedure. Extensive experiments have demonstrated the efficiency and effectiveness of our proposed approach in answering PRank queries, in terms of both wall clock time and the number of candidates to be refined.
17679131
Efficient Methods on Predictions for Similarity Search over Stream Time Series
Due to the wide usage of stream time series, an efficient and effective similarity search over stream data becomes essential for many applications. Although many approaches have been proposed for searching through archived data, because of the unique characteristics of the stream, for example, data are frequently updated, traditional methods may not work for the stream time series. Especially, for the cases where the arrival of data is often delayed for various reasons, for example, the communication congestion or batch processing and so on, queries on such incomplete time series or even future time series may result in inaccuracy. Therefore, in this paper we propose two approaches, polynomial and probabilistic, to predict the unknown values that have not arrived at the system. We also present efficient indexes, that is, a multidimensional hash index and B+-tree, to facilitate the prediction and similarity search on future time series, respectively. Extensive experiments demonstrate the efficiency and effectiveness of our methods in terms of I/O, prediction and query accuracy
2677048
Convergence analysis of convex incremental neural networks
Recently, a convex incremental algorithm (CI-ELM) has been proposed in Huang and Chen (Neurocomputing 70:3056–3062, 2007), which randomly chooses hidden neurons and then analytically determines the output weights connecting with the hidden layer and the output layer. Though hidden neurons are generated randomly, the network constructed by CI-ELM is still based on the principle of universal approximation. The random approximation theory breaks through the limitation of most conventional theories, eliminating the need for tuning hidden neurons. However, due to the random characteristic, some of the neurons contribute little to decrease the residual error, which eventually increase the complexity and computation of neural networks. Thus, CI-ELM cannot precisely give out its convergence rate. Based on Lee’s results (Lee et al., IEEE Trans Inf Theory 42(6):2118–2132, 1996), we first show the convergence rate of a maximum CI-ELM, and then systematically analyze the convergence rate of an enhanced CI-ELM. Different from CI-ELM, the hidden neurons of the two algorithms are chosen by following the maximum or optimality principle under the same structure as CI-ELM. Further, the proof process also demonstrates that our algorithms achieve smaller residual errors than CI-ELM. Since the proposed neural networks remove these “useless” neurons, they improve the efficiency of neural networks. The experimental results on benchmark regression problems will support our conclusions.