29766053
Construction for bicritical graphs and k-extendable bipartite graphs
A graph G is said to be bicritical if G-u-v has a perfect matching for every choice of a pair of points u and v. Bicritical graphs play a central role in decomposition theory of elementary graphs with respect to perfect matchings. As Plummer pointed out many times, the structure of bicritical graphs is far from completely understood. This paper presents a concise structure characterization on bicritical graphs in terms of factor-critical graphs and transversals of hypergraphs. A connected graph G with at least 2k+2 points is said to be k-extendable if it contains a matching of k lines and every such matching is contained in a perfect matching. A structure characterization for k-extendable bipartite graphs is given in a recursive way. Furthermore, this paper presents an O(mn) algorithm for determining the extendability of a bipartite graph G, the maximum integer k such that G is k-extendable, where n is the number of points and m is the number of lines in G.
17170240
The Z-Transformation graph for an outerplane bipartite graph has a Hamilton path
The Z-transformation graph of perfect matchings of a plane bipartite graph G has the perfect matchings of G as vertices, two perfect matchings being adjacent if their symmetric difference forms a cycle that is the boundary of an interior face of G. In this note, we prove that the Z-transformation graph of perfect matchings of an outerplane bipartite graph has a Hamilton path.
15887745
The Rotation Graphs of Perfect Matchings of Plane Bipartite Graphs
Abstract In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC systems and perfect matchings in G.
39584893
A solution to Gutman's problem on the characteristic polynomial of a bipartite graph
Abstract In this short paper, we present a solution to Gutman's problem on the characteristic polynomial of a bipartite graph (Research Problem 134, Discrete Math. 88 (1991)).
11228203
k-factor-covered Regular Graphs
11755901
Interactive mesh deformation with pseudo material effects
This paper presents a novel interactive mesh deformation method that can achieve various dynamic material effects, including elastic membrane and cloth effects. In our framework, a mesh is encoded by some differential quantities based on edge length and dihedral angle; and the deformation is formulated as a least square problem for preserving the edge length and dihedral angle via the differential quantities. In order to obtain anisotropic material effects, we further propose an edge-weighting scheme based on a user-specified vector field. To avoid specifying the local transformations, we set up an iterative scheme for solving the deformation. At last, several examples are presented to show that our approach can interactively generate visually pleasing deformations. Copyright © 2006 John Wiley & Sons, Ltd.
1131614
Meta-Evaluation of Image Segmentation Using Machine Learning
Image segmentation is a fundamental step in many computer vision applications. Generally, the choice of a segmentation algorithm, or parameterization of a given algorithm, is selected at the application level and fixed for all images within that application. Our goal is to create a stand-alone method to evaluate segmentation quality. Stand-alone methods have the advantage that they do not require a manually-segmented reference image for comparison, and can therefore be used for real-time evaluation. Current stand-alone evaluation methods often work well for some types of images, but poorly for others. We propose a meta-evaluation method in which any set of base evaluation methods are combined by a machine learning algorithm that coalesces their evaluations based on a learned weighting function, which depends upon the image to be segmented. The training data used by the machine learning algorithm can be labeled by a human, based on similarity to a human-generated reference segmentation, or based upon system-level performance. Experimental results demonstrate that our method performs better than the existing stand-alone segmentation evaluation methods.
7692801
Semi-quantitative Simulation Modeling of Software Engineering Process
Software process simulation models hold out the promise of improving project planning and control. However, purely quantitative models require a very detailed understanding of the software process, i.e. process knowledge represented quantitatively. When such data is lacking, quantitative models impose severe constraints, restricting the model's value. In contrast, qualitative models display all possible behaviors but only in qualitative terms. This paper illustrates the value and flexibility of semi-quantitative modeling by developing a model of the software staffing process and comparing it with other quantitative staffing models. We show that the semi-quantitative model provides more insights into the staffing process and more confidence in the outcomes than the quantitative models by achieving a tradeoff between quantitative and qualitative simulation. In particular, the semi-quantitative simulation produces a set of possible outcomes with the ranges of real numeric values. The semi-quantitative model allows us to determine the solution boundaries for specific scenarios under the conditions of limited knowledge.
2426049
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions
15559062
Adaptive Geometry Compression Based on 4-Point Interpolatory Subdivision Schemes
We propose an adaptive geometry compression method based on 4-point interpolatory subdivision schemes. It can work on digital curves of arbitrary dimensions. With the geometry compression method, a digital curve is adaptively compressed into several segments with different compression levels. Each segment is a 4-point subdivision curve with a subdivision step. In the meantime, we provide high-speed 4-point interpolatory subdivision curve generation methods for efficiently decompressing the compressed data. In the decompression methods, we consider both the open curve case and the closed curve case. For an arbitrary positive integer k, formulae of the number of the resultant control points of an open or closed 4-point subdivision curve after k subdivision steps are provided. The time complexity of the new approaches are O(n), where n is the number of the points in the given digital curve. Examples are provided as well to illustrate the efficiency of the proposed approaches.