34749580
Plane elementary bipartite graphs
A connected graph is called elementary if the union of all perfect matchings forms a connected subgraph. In this paper we mainly study various properties of plane elementary bipartite graphs so that many important results previously obtained for hexagonal systems are treated in a unified way. Firstly, we show that a plane bipartite graph G is elementary if and only if the boundary of each face (including the infinite face) is an alternating cycle with respect to some perfect matching of G. For a plane bipartite graph G all interior vertices of which are of the same degree, a stronger result is obtained; namely, G is elementary if and only if the boundary of the infinite face of G is an alternating cycle with respect to some perfect matching of G. Second, the concept of the Z-transformation graph Z(G) of a hexagonal system G (whose vertices represent the perfect matchings of G) is extended to a plane bipartite graph G and some results analogous to those for hexagonal systems are obtained. A peripheral face f of G is called reducible if the removal of the internal vertices and edges of the path that is the intersection of f and the exterior face of G results in a plane elementary bipartite graph. Thirdly, we obtain the reducible face decomposition for plane elementary bipartite graphs. Furthermore, sharp upper and lower bounds for the number of reducible faces are derived. Conversely, we can construct any plane elementary bipartite graphs by adding new peripheral faces one by one. As applications of this approach, we give simple construction methods for several types of plane elementary bipartite graphs G that contain a forcing edge (which belongs to exactly one perfect matching of G) and whose Z-transformation graphs Z(G) contain vertices of degree one.
41201857
A Note on the Number of Perfect Matchings of Bipartite Graphs
Abstract Let G be a bipartite graph with 2n vertices, A its adjacency matrix and K the number of perfect matchings. For plane bipartite graphs each interior face of which is surrounded by a circuit of length 4s + 2, s ϵ {1, 2, …}, an elegant formula, i.e. det A = (−1)nK2, had been rigorously proved by Cvetkovic et al. (1982). For general bipartite graphs, this note contains a necessary and sufficient condition for the above relation to hold. A fast algorithm to check if a plane bipartite graph has such a relation is given.
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.
207679368
A Distributive Lattice on the Set of Perfect Matchings of a Plane Bipartite Graph
Let G be a plane bipartite graph and M(G) the set of perfect matchings of G. The Z-transformation graph of G is defined as a graph on M(G): M,M′∈M(G) are joined by an edge if and only if they differ only in one cycle that is the boundary of an inner face of G. A property that a certain orientation of the Z-transformation graph of G is acyclic implies a partially ordered relation on M(G). An equivalent definition of the poset M(G) is discussed in detail. If G is elementary, the following main results are obtained in this article: the poset M(G) is a finite distributive lattice, and its Hasse diagram is isomorphic to the Z-transformation digraph of G. Further, a distributive lattice structure is established on the set of perfect matchings of any plane bipartite graph.
46427487
The Clar Covering Polynomial of Hexagonal Systems I
Abstract In this paper the Clar covering polynomial of a hexagonal system is introduced. In fact it is a kind of F polynomial [4] of a graph, and can be calculated by recurrence relations. We show that the number of aromatic sextets (in a Clar formula), the number of Clar formulas, the number of Kekule structures and the first Herndon number for any Kekulean hexagonal system can be easily obtained by its Clar covering polynomial. In addition, we give some theorems to calculate the Clar covering polynomial of a hexagonal system. As examples we finally derive the explicit expressions of the Clar covering polynomials for some small hexagonal systems and several types of catacondensed hexagonal systems. A relation between the resonance energy and the Clar covering polynomial of a hexagonal system is considered in the next paper.
44874837
Z-transformation graphs of perfect matchings of plane bipartite graphs
Abstract Let G be a plane bipartite graph with at least two perfect matchings. The Z -transformation graph, Z F ( G ), of G with respect to a specific set F of faces is defined as a graph on the perfect matchings of G such that two perfect matchings M 1 and M 2 are adjacent provided M 1 and M 2 differ only in a cycle that is the boundary of a face in F . If F is the set of all interior faces, Z F ( G ) is the usual Z -transformation graph; If F contains all faces of G it is a novel graph and called the total Z -transformation graph. In this paper, we give some simple characterizations for the Z -transformation graphs to be connected by applying the above new idea. Furthermore, we show that the total Z -transformation graph of G is 2-connected if G is elementary; the total Z -transformation digraph of G is strongly connected if and only if G is elementary.
5976625
Augmenting naive Bayes for ranking
Naive Bayes is an effective and efficient learning algorithm in classification. In many applications, however, an accurate ranking of instances based on the class probability is more desirable. Unfortunately, naive Bayes has been found to produce poor probability estimates. Numerous techniques have been proposed to extend naive Bayes for better classification accuracy, of which selective Bayesian classifiers (SBC) (Langley & Sage, 1994), tree-augmented naive Bayes (TAN) (Friedman et al., 1997), NBTree (Kohavi, 1996), boosted naive Bayes (Elkan, 1997), and AODE (Webb et al., 2005) achieve remarkable improvement over naive Bayes in terms of classification accuracy. An interesting question is: Do these techniques also produce accurate ranking? In this paper, we first conduct a systematic experimental study on their efficacy for ranking. Then, we propose a new approach to augmenting naive Bayes for generating accurate ranking, called hidden naive Bayes (HNB). In an HNB, a hidden parent is created for each attribute to represent the influences from all other attributes, and thus a more accurate ranking is expected. HNB inherits the structural simplicity of naive Bayes and can be easily learned without structure learning. Our experiments show that HNB outperforms naive Bayes, SBC, boosted naive Bayes, NBTree, and TAN significantly, and performs slightly better than AODE in ranking.
760636
Accelerated occlusion culling using shadow frusta
Many applications in computer graphics and virtual environments need to render datasets with large numbers of primitives and high depth complexity at interactive rates. However, standard techniques like view frustum culling and a hardware z-bu er are unable to display datasets composed of hundred of thousands of polygons at interactive frame rates on current high-end graphics systems. We add a \conservative"visibility culling stage to the rendering pipeline, attempting to identify and avoid processing of occluded polygons. Given a moving viewpoint, the algorithm dynamically chooses a set of occluders. Each occluder is used to compute a shadow frustum, and all primitives contained within this frustumare culled. The algorithmhierarchicallytraverses the model, culling out parts not visible from the current viewpoint using e cient, robust, and in some cases specialized interference detection algorithms. The algorithm's performance varies with the location of the viewpoint and the depth complexity of the model. In the worst case it is linear in the input size with a small constant. In this paper, we demonstrate its performance on a city model composed of 500;000 polygons and possessing varying depth complexity. We are able to cull an average of 55% of the polygons that would not be culled by view-frustum culling and obtain a commensurate improvement in frame rate. The overall approach is e ective and scalable, is applicable to all polygonal models, and can be easily implemented on top of view-frustum culling.
9641517
Alignment of BLAST High-scoring Segment Pairs Based on the Longest Increasing Subsequence Algorithm
MOTIVATION
The popular BLAST algorithm is based on a local similarity search strategy, so its high-scoring segment pairs (HSPs) do not have global alignment information. When scientists use BLAST to search for a target protein or DNA sequence in a huge database like the human genome map, the existence of repeated fragments, homologues or pseudogenes in the genome often makes the BLAST result filled with redundant HSPs. Therefore, we need a computational strategy to alleviate this problem.


RESULTS
In the gene discovery group of Celera Genomics, I developed a two-step method, i.e. a BLAST step plus an LIS step, to align thousands of cDNA and protein sequences into the human genome map. The LIS step is based on a mature computational algorithm, Longest Increasing Subsequence (LIS) algorithm. The idea is to use the LIS algorithm to find the longest series of consecutive HSPs in the BLAST output. Such a BLAST+LIS strategy can be used as an independent alignment tool or as a complementary tool for other alignment programs like Sim4 and GenWise. It can also work as a general purpose BLAST result processor in all sorts of BLAST searches. Two examples from Celera were shown in this paper.
39496103
An Application of Well-orderly Trees in Graph Drawing
Well-orderly tree is a powerful technique capable of deriving new results in graph encoding, graph enumeration and graph generation [3, 5]. In this paper, by using well-orderly trees, we prove that any plane graph G with n vertices has a visibility representation with height , which can be constructed in linear time. This improves the best previous bound of .
16350167
Efficient propagation for face annotation in family albums
In this paper, we propose and investigate a new user scenario for face annotation, in which users are allowed to multi-select a group of otogras and assign names to these otogras. The system will then attempt to propagate names from otogra level to face level, i.e. to infer the correspondence between name and face. Given the face similarity measure which combines methodologies from face recognition and content-based image retrieval, we formulate name propagation as an optimization problem. We define the objective function as the sum of similarities between each pair of faces of the same individual in different otogras, and propose an iterative optimization algorithm to infer the optimal correspondence. To make the propagation result reliable, a reject scheme is adopted to reject those with low confidence scores. Furthermore, we investigate the combination and alternation of browsing mode for propagation and viewer mode for annotation, so that each mode can benefit from additional inputs from the other mode. The experimental evaluation has been conducted within a typical family album of over one thousand otogras and the results show that the proposed approach is effective and efficient in automated face annotation in family albums.