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.
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.
34996713
Polynomial Time Solvability Of The Weighted Ring Arc-Loading Problem With Integer Splitting
In the Weighted Ring Arc-Loading Problem with Integer Splitting, we are given a set of communication requests each associated with a non-negative integer weight. The problem is to find a routing scheme such that the maximum load on arcs of the ring is minimized, subject to that the weight of each request may be split into two integral parts routed in two directions around the ring, where the load of an arc is the sum of parts routed through the arc. A pseudo-polynomial algorithm for this problem is implied by a result in [G. Wilfong and P. Winkler, Ring routing and wavelength translation, Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, San Fancisco, CA, 1998, 333-341]. By refining the rounding technique developed in the same paper, we prove that the problem can be solved in polynomial time.
32007375
Interpolation theorems for graphs, hypergraphs and matroids
Abstract Let P and Q be, respectively, hereditary and cohereditary properties defined on the subsets of a finite set S . We first prove that several functions related to P and Q interpolate over some families of subsets of S . By using this we then derive a number of interpolation results for graphs, hypergraphs and matroids.
35890566
On Isomorphisms of Minimal Cayley Graphs and Digraphs
Abstract. A Cayley graph or digraph Cay(G,S) is called a CI-graph of G if, for any T⊂G, Cay(G,S)≅Cay(G,T) if and only if Sσ=T for some σ∈Aut(G). The aim of this paper is to characterize finite abelian groups for which all minimal Cayley graphs and digraphs are CI-graphs.
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.
61202442
Probabilistic identity characterization for face recognition
We present a general framework for characterizing the object identity in a single image or a group of images with each image containing a transformed version of the object, with applications to face recognition. In terms of the transformation, the group is made of either many still images or frames of a video sequence. The object identity is either discrete- or continuous-valued. This probabilistic framework integrates all the evidence of the set and handles the localization problem, illumination and pose variations through subspace identity encoding. Issues and challenges arising in this framework are addressed and efficient computational schemes are presented. Good face recognition results using the PIE database are reported.
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.
135505
Image based regression using boosting method
We present a general algorithm of image based regression that is applicable to many vision problems. The proposed regressor that targets a multiple-output setting is learned using boosting method. We formulate a multiple-output regression problem in such a way that overfitting is decreased and an analytic solution is admitted. Because we represent the image via a set of highly redundant Haar-like features that can be evaluated very quickly and select relevant features through boosting to absorb the knowledge of the training data, during testing we require no storage of the training data and evaluate the regression function almost in no time. We also propose an efficient training algorithm that breaks the computational bottleneck in the greedy feature selection process. We validate the efficiency of the proposed regressor using three challenging tasks of age estimation, tumor detection, and endocardial wall localization and achieve the best performance with a dramatic speed, e.g., more than 1000 times faster than conventional data-driven techniques such as support vector regressor in the experiment of endocardial wall localization.
728
Analyzing and modelling the AS-level Internet topology
Recently we introduced the rich-club phenomenon as a quantitative metric to characterize the tier structure of the Autonomous Systems level Internet topology (AS graph) and we proposed the Interactive Growth (IG) model, which closely matches the degree distribution and hierarchical structure of the AS graph and compares favourble with other available Internet power-law topology generators. Our research was based on the widely used BGP AS graph obtained from the Oregon BGP routing tables. Researchers argue that Traceroute AS graph, extracted from the traceroute data collected by the CAIDA's active probing tool, Skitter, is more complete and reliable. To be prudent, in this paper we analyze and compare topological structures of Traceroute AS graph and BGP AS graph. Also we compare with two synthetic Internet topologies generated by the IG model and the well-known Barabasi-Albert (BA) model. Result shows that both AS graphs show the rich-club phenomenon and have similar tier structures, which are closely matched by the IG model, however the BA model does not show the rich-club phenomenon at all.
1717304
Shape Regression Machine
We present a machine learning approach called shape regression machine (SRM) to segmenting in real time an anatomic structure that manifests a deformable shape in a medical image. Traditional shape segmentation methods rely on various assumptions. For instance, the deformable model assumes that edge defines the shape; the Mumford-Shah variational method assumes that the regions inside/outside the (closed) contour are homogenous in intensity; and the active appearance model assumes that shape/appearance variations are linear. In addition, they all need a good initialization. In contrast, SRM poses no such restrictions. It is a two-stage approach that leverages (a) the underlying medical context that defines the anatomic structure and (b) an annotated database that exemplifies the shape and appearance variations of the anatomy. In the first stage, it solves the initialization problem as object detection and derives a regression solution that needs just one scan in principle. In the second stage, it learns a nonlinear regressor that predicts the nonrigid shape from image appearance. We also propose a boosting regression approach that supports real time segmentation. We demonstrate the effectiveness of SRM using experiments on segmenting the left ventricle endocardium from an echocardiogram of an apical four chamber view.