32852823
Restricted Edge Connectivity of Edge Transitive Graphs
16327244
Semi-hyper-connected edge transitive graphs
A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characterize semi-hyper-connected edge transitive graphs.
3006898
A six-color theorem for the edge-face coloring of plane graphs
Abstract It was shown (Kronk and Mitchen, 1973) that the set of vertices, edges and faces of any normal map on the sphere can be colored with seven colors. In this paper we solve a somewhat different problem: the set of edges and faces of any plane graph with Δ ⩽ 3 can be colored by six colors.
5156351
Model-based bundle adjustment with application to face modeling
We present a new model-based bundle adjustment algorithm to recover the 3D model of a scene/object from a sequence of images with unknown motions. Instead of representing scene/object by a collection of isolated 3D features (usually points), our algorithm uses a surface controlled by a small set of parameters. Compared with previous model-based approaches, our approach has the following advantages. First instead of using the model space as a regularizer we directly use it as our search space, thus resulting in a more elegant formulation with fewer unknowns and fewer equations. Second, our algorithm automatically associates tracked points with their correct locations on the surfaces, thereby eliminating the need for a prior 2D-to-3D association. Third, regarding face modeling, we use a very small set of face metrics (meaningful deformations) to parameterize the face geometry, resulting in a smaller search space and a better posed system. Experiments with both synthetic and real data show that this new algorithm is faster, more accurate and more stable than existing ones.
45941410
The optimal service time allocation of a versatile server to queue jobs and stochastically available non-queue jobs of different types
Abstract In this paper, we consider a service system in which the server can process N + 1 different types of jobs. Jobs of type 0 are generated randomly according to a Poisson stream. Jobs of types 1 to N are non-queue types which may or may not be available for completion by the server. To optimally allocate the server's time to these jobs, we formulate a finite state semi-Markov decision process model to this environment. With this model, the optimal stationary policies can be numerically determined via a policy-iteration algorithm. We also discuss the practical applications of this model to tele-service and tele-marketing operations.
17488685
Large deviations and the generalized processor sharing scheduling for a two-queue system
We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks.
38207892
On the Relations Between Arboricity and Independent Number Or Covering Number
In this paper, the following results are obtained: a(G) + β(G) ⩽ p + 1, ⌈p2⌉ ⩽ a(G)β(G), ⌈p2⌉ ⩽ a′(G) + gb′(G) ⩽ pa′(G) + α′(G) ⩽ 2⌈p2⌉ (δ ⩽ 1) and all bounds are sharp, where p = ¦V(G)¦, ⌈x⌉ denotes the smallest integer greater than or equal to x, a(G) is the vertex arboricity, a′(G) is the edge arboricity, α′(G) is the edge covering number, β(G) is the vertex independent number, β′(G) is the edge independent number, and δ is the minimum degree of G.