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.
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.
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.
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.)
11542871
Illuminating light field: image-based face recognition across illuminations and poses
We present an image-based method for face recognition across different illuminations and different poses, where the term 'image-based' means that only 2D images are used and no explicit 3D models are needed. As face recognition across illuminations and poses involves three factors, namely identity, illumination, and pose, generalizations from known identities to novel identities, from known illuminations to novel illuminations, and from known poses to unknown poses are desired. Our approach, called the illuminating light field, derives an identity signature that is invariant to illuminations and poses, where a subspace encoding is assumed for the identity, a Lambertain reflectance model for the illumination, and a light field model for the poses. Experimental results using the PIE database demonstrate the effectiveness of the proposed approach.
13349007
Greedy Algorithms for Client Assignment in Large-Scale Distributed Virtual Environments
Distributed Virtual Environments (DVEs), such as online games, military simulations, collaborative design, etc., are very popular nowadays. To support large-scale DVEs, a multi-server architecture is usually employed, and the virtual world is partitioned into multiple zones for load distribution. The client assignment problem arises when assigning the participating clients to the servers. Current approaches usually assign clients to servers according to the locations of clients in the virtual world, i.e., clients interacting in the same zone of the virtual world will be assigned to the same server. This approach may degrade the interactivity of DVEs if the network delay from a client to its assigned server is large. In this paper, we formulate the client assignment problem, and propose two algorithms to assign clients to servers in a more efficient way. The proposed algorithms are based on the heuristics developed for the well-known Terminal Assignment problem. Simulation results with the BRITE Internet Topology Generator show that our algorithms are effective in enhancing the interactivity of DVEs.
62771282
Robust appearance-based tracking of moving object from moving platform
We present a robust algorithm for tracking moving objects from a moving platform. Robustness is achieved by incorporating temporal differencing and shape detection in an appearance-based object tracking algorithm. In addition, the incorporation of these two methods also improves accuracy and computational efficiency of detection. Some experimental results using airborne-video tracking are given to illustrate the effectiveness of this method.
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.
13962685
Intra-personal kernel space for face recognition
Intra-personal space modeling proposed by Moghaddam et al. has been successfully applied in face recognition. In their work the regular principal subspaces are derived from the intra-personal spacce using a principal componen analysis and embedded in a probabilistic formulation. In this paper, we derive the principal subspace from the intro-personal kernel space by developing a probabilistic analysis for kernel principal components for face recognition. We test this algorithm on a subset of the FERET database with illumination and facial expression variations. The recognition performance demonstrates its advantage over other traditional subspace approaches.