25346055
Almost Covers Of 2-Arc Transitive Graphs
Let Γ be a G-symmetric graph whose vertex set admits a nontrivial G-invariant partition ℬ with block size v. Let Γℬ be the quotient graph of Γ relative to ℬ and Γ[B,C] the bipartite subgraph of Γ induced by adjacent blocks B,C of ℬ. In this paper we study such graphs for which Γℬ is connected, (G, 2)-arc transitive and is almost covered by Γ in the sense that Γ[B,C] is a matching of v-1 ≥ 2 edges. Such graphs arose as a natural extremal case in a previous study by the author with Li and Praeger. The case Γℬ ≅Kv+1 is covered by results of Gardiner and Praeger. We consider here the general case where Γℬ ≇Kv+1, and prove that, for some even integer n ≥ 4, Γℬ is a near n-gonal graph with respect to a certain G-orbit on n-cycles of Γℬ. Moreover, we prove that every (G, 2)-arc transitive near n-gonal graph with respect to a G-orbit on n-cycles arises as a quotient Γℬ of a graph with these properties. (A near n-gonal graph is a connected graph Σ of girth at least 4 together with a set ℰ of n-cycles of Σ such that each 2-arc of Σ is contained in a unique member of ℰ.)
18154847
Dynamic domination in fuzzy causal networks
This paper presents a dynamic domination theory for fuzzy causal networks (FCN). There are three major contributions. First, we propose a new inference procedure based on dominating sets. Second, we introduce the concepts of dynamic and minimal dynamic dominating sets (DDS and MDDS) in an FCN. To reflect changes of dominance with time, we also introduce the concept of a dynamic dominating process (DDP) that has significant implications in many real-world problems. We pay a special attention to the minimal dynamic dominating process (MDDP) and develop rules for generating DDP and MDDP. Third, we investigate dynamic dominating sets with extended feedback, which we call effective dynamic dominating sets (EDDS), and related effective dynamic dominating process (EDDP). This study unveils a very important phenomenon in FCN: At any time t, either an EDDS exists or there is a dramatic change of the states of vertices. In the latter case we also identify the special structure of the sub-FCN induced by active vertices.
8520561
Bounding the bandwidths for graphs
Let G;H be nite graphs with jV(H)j>jV(G)j. The bandwidth of G with respect to H is dened to be BH(G) = minmaxuv2E(G)dH((u);(v)), with the minimum taken over all injections from V(G )t oV(H), where dH(x;y) is the distance in H between two vertices x;y 2 V(H). This number is involved with the VLSI design and optimization, especially when the \host" graph H is a path Pn or a cycle Cn of length n = jV(G)j. In these two cases, BH(G) is known to be the ordinary bandwidth B(G) and the cyclic bandwidth Bc(G), respectively, and the corresponding decision problem is NP-complete. So estimations of B(G), Bc(G) and in general BH(G) are needed, especially in determining the bandwidths of some specic graphs. In this paper, we rst propose a systematic method for obtaining lower bounds for the bandwidth BH(G). By using this method, we then get a number of lower bounds for B(G) and Bc(G )i n terms of some distance- and degree-related parameters. c 2000 Elsevier Science B.V. All rights reserved.
38623555
Domination number and neighbourhood conditions
Abstract The domination number γ of a graph G is the minimum cardinality of a subset D of vertices of G such that each vertex outside D is adjacent to at least one vertex in D . For any subset A of the vertex set of G , let ∂ + ( A ) be the set of vertices not in A which are adjacent to at least one vertex in A . Let N (A) be the union of A and ∂ + ( A ), and d ( A ) be the sum of degrees of all the vertices of A . In this paper we prove the inequality 2q ⩽ (p−γ)(p−γ+2)−|∂ + (A)| (p−γ+1)+d( N (A)) , and characterize the extremal graphs for which the equality holds, where p and q are the numbers of vertices and edges of G , respectively. From this we then get an upper bound for γ which generalizes the known upper bound γ⩽p+1− 2q+1 . Let I ( A ) be the set of vertices adjacent to all vertices of A , and I (A) be the union of A and I ( A ). We prove that 2q ⩽ (p − γ − | I (A)| + 2)(p − γ + 4) + d( I (A)) − min {p − γ − | I (A)| + 2, |A|, |I(A)|, 3} , which implies an upper bound for γ as well.
14537383
Constructing a Class of Symmetric Graphs
We find a natural construction of a large class of symmetric graphs from point- and block-transitive 1-designs. The graphs in this class can be characterized as G -symmetric graphs whose vertex sets admit a G -invariant partition B of block size at least 3 such that, for any two blocks B, C of B, either there is no edge between B and C, or there exists only one vertex in B not adjacent to any vertex inC . The special case where the quotient graph ?Bof ? relative to B is a complete graph occurs if and only if the 1-design needed in the construction is a G -doubly transitive and G -block-transitive 2-design, and in this case we give an explicit classification of ? when G is a doubly transitive projective group or an affine group containing the affine general group. Examples of such graphs include cross ratio graphs studied recently by Gardiner, Praeger and Zhou and some other graphs with vertices the (point, line)-flags of the projective or affine geometry.
20645165
Harper-type lower bounds and the bandwidths of the compositions of graphs
Abstract We give a general Harper-type lower bound for the bandwidth of a graph which is a common generalization of several known results. As applications we get a lower bound for the bandwidth of the composition of two graphs. By using this we determine the bandwidths of some composition graphs such as ( P r × P s )[ H ], ( P r × C s )[ H ] (2 r ≠ s ), ( C r × C s )[ H ] (6 ⩽ 2 r ⩽ s ), etc., for any graph H . Interestingly, the bandwidths of these graphs have nothing to do with the structure of H in general.
3804246
The missing links in the BGP-based AS connectivity maps
PAM2003 - The Passive and Active Measurement Workshop(http://www.pam2003.org), San Diego, USA, April 2003
17046861
Appearance modeling under geometric context
We propose a unified framework based on a general definition of geometric transform (GeT) for modeling appearance. GeT represents the appearance by applying designed functionals over certain geometric sets. We show that image warping, Radon transform, trace transform, etc. are special cases of our definition. Moreover, three different types of GeTs are designed to handle deformation, articulation and occlusion and applied to fingerprinting the appearance inside a contour. They include the contour-driven GeT, the feature curve based GeT and selecting functionals to model the appearance inside the convex hull of the contour. A multi-resolution representation that combines both shape and appearance information is also proposed. We apply our approach to image synthesis and object recognition. The proposed approach produces promising results when applied to fingerprinting the appearance of human and body parts despite the challenges due to articulated motion and deformations
15470334
Probabilistic recognition of human faces from video
Recognition of human faces using a gallery of still or video images and a probe set of videos is systematically investigated using a probabilistic framework. In still-to-video recognition, where the gallery consists of still images, a time series state space model is proposed to fuse temporal information in a probe video, which simultaneously characterizes the kinematics and identity using a motion vector and an identity variable, respectively. The joint posterior distribution of the motion vector and the identity variable is estimated at each time instant and then propagated to the next time instant, Marginalization over the motion vector yields a robust estimate of the posterior distribution of the identity variable. A computationally efficient sequential importance sampling (SIS) algorithm is developed to estimate the posterior distribution. Empirical results demonstrate that, due to the propagation of the identity variable over time, a degeneracy in posterior probability of the identity variable is achieved to give improved recognition. The gallery is generalized to videos in order to realize video-to-video recognition. An exemplar-based learning strategy is adopted to automatically select video representatives from the gallery, serving as mixture centers in an updated likelihood measure. The SIS algorithm is applied to approximate the posterior distribution of the motion vector, the identity variable, and the exemplar index, whose marginal distribution of the identity variable produces the recognition result. The model formulation is very general and it allows a variety of image representations and transformations. Experimental results using images/videos collected at UMD, NIST/USF, and CMU with pose/illumination variations illustrate the effectiveness of this approach for both still-to-video and video-to-video scenarios with appropriate model choices.
15698378
A Binary Decision Tree Implementation of a Boosted Strong Classifier
Viola and Jones [1] proposed the influential rapid object detection algorithm. They used AdaBoost to select from a large pool a set of simple features and constructed a strong classifier of the form {∑jαjhj(x) ≥ θ} where each hj(x) is a binary weak classifier based on a simple feature. In this paper, we construct, using statistical detection theory, a binary decision tree from the strong classifier of the above form. Each node of the decision tree is just a weak classifier and the knowledge of the coefficients αjis no longer needed. Also, the binary tree has a lot of early exits. As a result, we achieve an automatic speedup that always makes the rapid Viola and Jones algorithm rapider.
13254850
Profile guided management of code partitions for embedded systems
Researchers have proposed to divide embedded applications into code partitions and to download partitions on demand from a wireless code server to enable a diverse set of applications for very tightly constrained embedded systems. This paper describes a new approach for managing the request and storage of code partitions and we explore the benefits of our scheme.