2337601
Bipartite graphs with small third Laplacian eigenvalue
In this paper, all connected bipartite graphs are characterized whose third largest Laplacian eigenvalue is less than three. Moreover, the result is used to characterize all connected bipartite graphs with exactly two Laplacian eigenvalues not less than three, and all connected line graphs of bipartite graphs with the third eigenvalue of their adjacency matrices less than one.
9689230
Doubly stochastic matrices of trees
Abstract In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices II, Linear Multilinear Algebr. 45 (1998) 275–285].
17354053
Graphs with fourth Laplacian eigenvalue less than two
In this paper, all connected graphs with the fourth largest Laplacian eigenvalue less than two are determined, which are used to characterize all connected graphs with exactly three Laplacian eigenvalues no less than two. Moreover, we determine bipartite graphs such that the adjacency matrices of their line graphs have exactly three nonnegative eigenvalues.
15047459
Disjoint Triangles of a Cubic Line Graph
Abstract.In this paper, we prove that a cubic line graph G on n vertices rather than the complete graph K4 has vertex-disjoint triangles and the vertex independence number . Moreover, the equitable chromatic number, acyclic chromatic number and bipartite density of G are respectively.
5632028
On the Laplacian Spectra of Graphs
We first establish the relationship between the largest eigenvalue of the Laplacian matrix of a graph and its bipartite density. Then we present lower and upper bounds for the largest Laplacian eigenvalue of a graph in terms of its largest degree and diameter.
6465422
CAEP: Classification by Aggregating Emerging Patterns
Emerging patterns (EPs) are itemsets whose supports change significantly from one dataset to another; they were recently proposed to capture multi-attribute contrasts between data classes, or trends over time. In this paper we propose a new classifier, CAEP, using the following main ideas based on EPs: (i) Each EP can sharply differentiate the class membership of a (possibly small) fraction of instances containing the EP, due to the big difference between its supports in the opposing classes; we define the differentiating power of the EP in terms of the supports and their ratio, on instances containing the EP. (ii) For each instance t, by aggregating the differentiating power of a fixed, automatically selected set of EPs, a score is obtained for each class. The scores for all classes are normalized and the largest score determines t’s class. CAEP is suitable for many applications, even those with large volumes of high (e.g. 45) dimensional data; it does not depend on dimension reduction on data; and it is usually equally accurate on all classes even if their populations are unbalanced. Experiments show that CAEP has consistent good predictive accuracy, and it almost always outperforms C4.5 and CBA. By using efficient, border-based algorithms (developed elsewhere) to discover EPs, CAEP scales up on data volume and dimensionality. Observing that accuracy on the whole dataset is too coarse description of classifiers, we also used a more accurate measure, sensitivity and precision, to better characterize the performance of classifiers. CAEP is also very good under this measure.
11532289
Computing Complex Iceberg Cubes by Multiway Aggregation and Bounding
Iceberg cubing is a valuable technique in data warehouses. The efficiency of iceberg cube computation comes from efficient aggregation and effective pruning for constraints. In advanced applications, iceberg constraints are often non-monotone and complex, for example, “Average cost in the range [δ 1, δ 2] and standard deviation of cost less than β”. The current cubing algorithms either are efficient in aggregation but weak in pruning for such constraints, or can prune for non-monotone constraints but are inefficient in aggregation. The best algorithm of the former, Star-cubing, computes aggregations of cuboids simultaneously but its pruning is specific to only monotone constraints such as “COUNT(*) ≥ δ”. In the latter case, the Divide and Approximate pruning technique can prune for non-monotone constraints but is limited to bottom-up single-group aggregation. We propose a solution that exhibits both efficiency in aggregation and generality and effectiveness in pruning for complex constraints. Our bounding techniques are as general as the Divide and Approximate pruning techniques for complex constraints and yet our multiway aggregation is as efficient as Star-cubing.
8152868
A web-enabled video indexing system
Video parsing and indexing is an important early stage of content-based video analysis. In this paper, we present a new web-enabled video indexing system that integrates Synchronized Multimedia Integration Language (SMIL) standard. New algorithms are proposed for video temporal segmentation. Sharp transition detection is achieved by an enhanced histogram-based method that is robust to illumination changes. For gradual transition detection, new features are introduced for dissolve detection. The proposed dissolve detector is based on a combined analysis of mean-variance-skewness of intensity. Compared with existing variance-based approaches, the introduced new features improve the discrimination ability on shot boundaries. We also describe methods for eliminating false positives. Experimental results show that the proposed algorithms can effectively detect shot boundaries. Detected scenes and other cinematic attributes are structured and organized by integrating HTML and SMIL. For each video file, the system generates a table-of-contents indexing file. The user-friendly interface provides web-based interaction, browsing and previewing of video content
44391380
Bi-directional gradient labeling and registration for gray-scale image segmentation
Watershed is one of the commonly used methods for image segmentation. In this paper, we introduce a new segmentation scheme based on bi-directional labeling and registration and prove that its segmentation performance is equivalent to that of conventional watershed but it is much more computational efficient The bi-directional labeling and registration scheme, which will be referred to as BIDS, involves only linear scans of image pixels. It uses one dimensional operations instead of queues while traditional segmentation algorithms are two dimensional problems. BIDS also provides unique labels for each homogeneous regions. In addition to achieving the same segmentation results as conventional watershed, BIDS is four times less computationally complex than the conventional watersheds by immersion.
205875547
The hamiltonicity of bipartite graphs involving neighborhood unions
Let G = (X,Y) be a 2-connected balanced bipartite graph with |X| = |Y| = n. In this paper, we prove that if |N(x1) ∪ N(x2)| + |N(y1) ∪ N(y2)| ≥ n+2 for any {x1, x2} ⊆ X and {y1, y2} ⊆ Y, then G is hamiltonian except when G is a special graph on 8 or on 12 vertices.